I'm wondering if there is a way to add fictional science while still
feeling like science fiction.
What you are searching for is to make your fictional science plausible. I mean, to make your fictional science feel like real science, you do not really care if it will be possible or not, you just should make your reader believe it, while reading.
With that idea in mind, I will stress a couple of points, but note they are mainly based on my experience as a reader and are probably not universal. My reflection is based on the fact that there is fictional science that we are inclined to believe, and other that is problematic in our mind. I will try to make clear the difference between the two.
Do not explain what does not need to be
As long as your reader does not question himself about the reality of the science you are talking about, everything feels like real science. It is way more convincing to have a teleportation device, without explanation, than to have a teleportation device transmitting you through wires or waves, or anything. If you speak about wire, the reader will start to think about how is it possible to do it through wire, and the feeling that you are handwaving may arise.
Focus on details that impact the scenario
For Star Wars, and the destruction of the Death Star, the main point risen against plausibility (in my experience) is the fact that by shooting in a hole with a tiny spaceship you can destroy it, meaning the design of the Death Star is terribly bad. Questioning it is natural, since otherwise the rebels would have no way to win (more or less).
From a science point of view it is merely a detail, compare to the fact that the baddies just build a ship the size of a moon, that just destroyed a planet by firing green laser. Or the fact that a spherical ship would be a nightmare to cool down. Of the fact that it appears to be artificial gravity inside every ship.
But all this does not impact the scenario, so you are not pushed to question this point, so you will probably not.
Human stupidity is more unrealistic than fictional science
If at some point your reader think "they are all stupid, with that science they could just do that thing and it will be over", it will totally destroy the plausibility of your story. It destroyed Harry Potter for me : sorcerers could just merge science with magic but they do not because of... reasons. On the other hand I never questioned the possibility of magic while reading (this example is not exactly about science, but it illustrates my point quite well, I hope).
This point is also related to the fact that you should heavily investigate the consequences of the new science you introduce.