OK, so after a few weeks, I think I can come out with a "todo" list from this discussion and a few others. (Note, though inspired by many others, this is still largely my opinion)
1. One or two more balance passes of the fleet ships (this includes making sure that each fleet ship type has its own "feel")
2. Figure out what to do with starships (there are plenty of other good threads with good ideas talking about this)
3. Figure out how to make armor play a bigger role in battles (while still keeping it deterministic)
4. Tweak the balance of offense vs. defense (at standard difficulties (6-8, inclusive), the AI needs to do a good job keeping you back and threatening you, but not so much so that you don't get a chance to attack yourself) (close to being right, but still not quite there yet)
5. Figure out how to deal with the "focus fire makes big things less useful" effect
Less important todos:
6. Balance pass for the guard posts and guardians
7. Balance pass for the golems (armored, black widow, and regenerator in particular)
8. Balance pass for the spirecraft (though, pretty much only the shield bearer and the scout are left)
9. Introduce a little more variety to the Fallen Spire campaign minor faction
EDIT: Numbers 1 and 4 are probably the most important to solving the issue I originally highlighted, so those should probably be the focus once development resumes