Forgetting some of the throwaway lines like 'smaller animals will survive' issues in the question above, let's take a look at the specifics of ants and do some basic extrapolation on how they might evolve. But, in order to do that, we need to understand why they're successful in their current environment.
Ants, contrary to normal beliefs, wouldn't spend most of their time digging and foraging. The digging? Sure, there is some of that to be done, and the anthills that are built by ants are quite impressive, but remember that these are built over many generations of ants, because of the need to expand and support specific functions, like breeding.
Some anthills are designed (yes, designed) to incorporate a natural air conditioning model, often having a pool of water in them near air intakes before the hot air is extracted out the top via a chimney effect. For an unintelligent species, this is a pretty intelligent design and you'll find that over time, as the hill expands, this core design (and many other aspects of the ant-hill) are scaled up seamlessly as the colony grows. The point of all this being that while ants do grow their homes, it's not a core reason for them to exist.
As for foraging, it is true that some ants go looking for food, but once they've found it the far larger effort expenditure is retrieval. You don't have thousands of ants looking for food, you have thousands of ants carrying the food back once its found. But, it's important to note that ants aren't just gatherers. They're also farmers. Some species actually keep aphids almost like dairy cattle, using them as a source of honeydew. There's even ants out there that are mushroom farmers, essentially growing crops for the colony.
So, we have a species that seems to have a collective intelligence of some kind, that maintain a sophisticated homes, can manage crops and other animals, and have a foraging and retrieval cycle for their other food sources. How will they evolve?
One example of how that's happening is in the link you provided to Pharoah Ants. While many species of insects can only tolerate a single queen per colony, these ants have several and it seems to work well for them, even increasing genetic diversity within the colony. It is reasonably easy to extrapolate from such a feature that colonies could easily grow through mutual support at a rate that other insects may struggle with, especially in an environment of plentiful food and other resources.
Given that some ants already have wings, one other possible mutation would be in communication. It's generally believed that foraging ants leave a chemical trail to food on their way back which is how the retrieval corps gets organised so quickly. If your chemical could either;
1) Communicate location through abstract concepts, or
2) Be produced in higher volumes and dropped to the ground during flight,
your foragers could be winged, meaning they could cover a greater area. This would not be terribly dissimilar to what bees already do, but there would need to be a more detailed communication because the retrieval corps would likely not have flight capability so they would need a way to follow a ground trail explained by a flyer; not easy to do without dropping the chemical trail ala option 2.
Speaking of the retrieval corps, one of the benefits ants have in terms of their relative strength compared to body size is the square cube law. Basically what it says is that the volume of a creature increases exponentially to its size, meaning that the amount of effort it needs to apply in supporting itself as a percentage of the energy it can apply is greater. Put more simply, ants can support a great amount of weight by proportion to their body size specifically because they're small.
That said, that doesn't mean there isn't room for improvement. For one thing, they tend to carry things with their mandibles, not their legs. With stronger legs in the rear, they could develop grips on the soles of their forelegs, that could potentially be used to carry some light things. That's not viable as a scaleable option because 6 legs unless the segment holding the forelegs in their exoskeleton can bend sufficiently to make the ant appear to be standing upright, like a centaur. In the short term however stronger and larger mandibles are still likely to be the order of the day. So that means larger heads, larger mouths, and probably their forelegs moving slightly forward to support all this. In the long term, this could easily make them the strongest legs over time to counterbalance the weight they now carry in their mandibles. This would of course also make them more effective in inter-colony or inter-species combat.
The farming activities is the more interesting one. They may develop a little in size, and learn to domesticate other insects. They won't grow too much in size because otherwise their carapaces would have to alter a fair bit to ensure their current engineering doesn't get overwhelmed by the square cube law, but perhaps they could get big enough to domesticate some other species of insects other than aphids. Perhaps, if they get big enough, they could even domesticate some larger insects like cockroaches to act as a form of rideable animal. You could even have cavalry charges in combat with say termites, with the cokroaches providing an elevated platform from which the ants could strike.
All the above of course is pure speculation. I've just taken some of the traits I happen to know about in ants and extend them out to more optimal models. All this assumes of course a strong and steady food supply, but where environmental pressures tend to efficiency for reasons of competition, etc.
Being able to reproduce in greater numbers (multiple queens), being able to find food faster (aerial foragers), carry more of it in a single trip (larger mandibles) and domesticate more species are all existing pressures on ants that already drive their behaviours and their morphology. Whether or not any of this will come to pass is something beyond my ability to answer, but at the very least I hope I've given some food for thought.