There is no royal road

"How can I break down the task of resolving science-based issues into manageable chunks?"

There is really only one way to do it: learn how the world works, so that you know more about how the world works than your readers do. ("Readers" can be watchers, listeners, players and so on. The people to whom you are telling the story.) Note that the goal is not to accumulate more knowledge than most people, but simply to accumulate more knowledge than your target audience; and to use that knowledge to create a world that your audience believes.

It is said that once upon a time the king of Egypt, Ptolemy something or other, asked Euclid how to approach learning geometry faster, so that he could balance his desire for knowledge with the performance of his kingly duties; Euclid answered back that there was no royal road to geometry.

This means that the general approach involves the following steps:

1. Have an idea for a story.

   This is the hardest part, and most people cannot do it. Your questions show that you are imaginative and able to come up with plenty of story ideas, so you are already way ahead.

2. Identify your audience.

   It is one thing to tell a story to a small child (Disney), another to tell a story to a pre-teen (Star Wars), yet another to tell it to a teen-ager (Star Trek) and yet another to tell it to an adult. In a story for small children the only requirement is plot consistency (i.e., don't forget who killed the dragon); in a story for pre-teens the world must make sense on the individual scale, but large scale consistency is irrelevant; in a story for teen-agers the world should make sense on human scale, because teen-agers have already figured out what makes people tick; but in a story for adults the world should be fully self-consistent, period.

   This is all about levels of consistency, of which more below.

3. Explain what you must in order to get the desired level of world consistency, but not more.

   This is important. Nobody is ever interested in more detail than it's needed for the story to work. When you read a story where there seems to be more detail that what is strictly needed, and yet you find yourself enjoying the story, you will soon realize that the apparently spurious details had actually a very good reason to be there; maybe they set up a larger story arc; maybe their purpose is ornamental; maybe they are actually comments on some aspect of the plot, or of the characters, which you have missed on first pass; but, if they do not detract from the enjoyment of the story it always means that they have a reason which you can find. Sometimes it is even the case that when you actually examine the apparently useless details you will realize that you have completely missed the real story, and that you need to go back and re-evaluate everything.

To summarize, assuming that you have already created or acquired a basic story idea, the next step is to identify the required level of consistency:

• Is this a story for small children? Then only simple plot consistency is needed.

  Think Little Red Riding Hood, Sleeping Beauty and so on. Everything goes, as long as you keep track of who said what and who did what.

• Is this a story for pre-teens? Then plot consistency is needed, and in addition the world must make sense on an individual's level. Physics can be twisted in any shape, as long as on an individual's scale things work as they really do.

  Star ships the size of a family car can go faster than light? Sure! A pre-teen knows that car-sized objects can travel fast from place to place, so this does not violate their assumptions. A tiny device hidden in a robot projects the three-dimensional moving talking picture of a pricess? Sure, but you need to explain that this is advanced technology. Pre-teens know that there is technology to have moving talking images, so this is a simple extension from their point of view.

• Is this a story for teen-agers? Then plot consistency is needed, the world must make sense on an individual's level, and in addition the world must make sense on human scales.

  No car-sized star ships. No light sabers. But big star ships? Sure! We have seen our rockets go to Mars and Jupiter and Saturn, and the story is in the future! Teen-agers expect that the crew of the Enterprise has to eat, so you need to explain where the food comes from; but they don't yet fully appreciate macro-economy, so you do not need to explain why the Federation exists and why it is expending a lot of effort and resources in maintaining a manned Star Fleet.

• Is this a story for adults? Then plot consistency is needed, the world must make sense on an individual's level, the world must make sense on human scales, and in addition the world must be fully self-consistent.

  The key part here is self-consistent. The world of the story does not have to be consistent with the real world; it must be consistent with itself. This is why science-fiction and fantasy stories are possible: readers are perfectly willing to accept any self-consistent world; but they rebel and leave bad reviews if they feel that they were cheated and the world of the story breaks self-consistency.

And here we come to the gist of your question: how to resolve science-based issues. What you need to do is to establish what science-based issues are there in the first place, and then learn enough about them so that you know how to address them. The point being that you do not need and you do not want to place all the aspects of your world in the science-based bucket. Remember that all you need is a self-consistent world. Some aspects of the fictional world are how they are because they are how they are, and that's it. Only the remaining aspects of the fictional world can go into the science-based bucket.

Examples

• Taylor Anderson's [Destroyermen], an entertaining parallel-world adventure series of novels, following the crew of an American Wickes-class destroyer which is displaced to a parallel timeline during the Second Battle of the Java Sea (March 1942); in that parallel timeline Earth is inhabited by two native sentient species, the warlike reptilian Grik and the relatively peaceful Lemurians, plus the humans brought there by several timeline-displacement events. Besides the expected military fantasy, it includes at least two rather cute and well-thought cross-species romances.

  The time displacement and sentient reptiles are not science-based issues. They just are. But the rest of the world presents plenty of science-based issues, and they are quite deftly solved. How does the crew of the the (real historical) USS Walker (DD-163) acquire fuel for their ship? How would a reptile which lacks lips pronounce English words? How to our WW2-era American crewmen adapt to life in a society of shapely Lemurians? How does an r-selected species which has a juvenile non-sentient life stage develop a functional society? Those are issues which need to be resolved consistently.

• David Drake and Eric Flint's Belisarius, an alternate history military SF adventure, featuring an evil AI sent back from the future to organize an Indian Empire and take over the world, and a good (but much less powerful) AI sent to the Roman Empire of Justinian and Theodora to help the real historical general Flavius Belisarius to fight against the forces of evil.

  The two AIs are not science-based issues. They just are. Moreover, to make for an interesting plot, the good AI is weak, small, and the only superpower it has is to be able to speak telepathically to Belisarius himself. (Actually, to speak telepathically to one person, selected by a process similar to imprinting; it was lucky that the person who found it did not keep it for himself but gave it to Belisarius.) No long-distance vision, no weapons, no teleportation.

  This sets up an entertaining conflict, in which Aide (the good AI) and Belisarius must co-operate closely if they are to be successful against the existential threat. Plenty of science-based questions remain to be solved, because the rest of the world must still work as the real world does. How to set in motion an arms race in the 6th century Eastern Roman empire? How to resolve the real historical rift between the mainline orthodoxy and the monophysite heresy which risked splitting the Empire? How to acquire a naval power in the Indian ocean? How to fight a successful war in Mesopotamia against a large invasion force, complete with reasonably good logistics and crude gunpowder artillery?

• David Weber's Honorverse, a sprawling and very tightly plotted space opera / military SF series, set in a world where two kinds of FTL travel and one kind of FTL communications are available.

  Again, the FTL travel (by means of wormholes and / or Warshawski sails) and FTL communications (by means of grav pulses) just are. They are, they are not explained in any serious way, and nobody cares. But the rest of the world has to be consistent; battles must make sense (the series has been called "missile porn" for the loving detail in which battle tactics are presented), the economic base must make sense (albeit with a massive right-wing "neoconservative" bent, but hey, it's consistent), people must act like people actually act, and so on.

  This is a good example of following through with the not-real-world aspects of the fictional world. Medical science is very advanced, so that most people can have any injury repaired by regeneration; but what happens to those few on whom this doesn't work? How does society treat them? How do they perceive themselves? Humans are friends with a race of sentient telepathic cats. How does a society of telepaths view non-telepathic humans? What happens when a member of a telepathic race loses this ability? In a world where technology by and large has solved all basic necessities of life, can there be dictatorship and perceived poverty? (Yes, and yes.) How can human society thrive on a poisonous planet? (With difficulty and compromise.) And so on. (Ah, and did I mention that it is tightly plotted?)

• John Scalzi's Old Man's War series is a very good example of how well can a good, thoroughly verisimilar story be set in a most fantastic world. Since the first book of this series was published in the 21st century I will avoid any spoilers, but know that it features bionic enhancements, resurrection, AI implants and so on -- and yet it remains self-consistent, and keeps the characters profoundly realistic.

Now we shouldn't assume that this approach of building a self-consistent world by merging the real world with one or two or three unexplainable fantastic elements is new; it is not new, it is three thousand years old. Think of Homer's Iliad, which can be seen as the sort of military SF a genius would write in the 9th (or 8th, or 7th, we don't know) century before the common era. There are gods who intervene directly and personally in human affairs; the notoriously quarrelsome Greeks are united under a common leadership against an external foe; some of the characters have superpowers: this is just how it is, Homer does not explain where the gods come from, or how come that Greece has a paramount king. But the rest of the world is thoroughly self-consistent and realistic: in the end, the Iliad is an exemplary story about the power of love and friendship and the dire consequences of a serious managerial mistake.