TAS most definitely increases. In a round about way, I was talking about
IAS. My understanding, and I'm pretty sure of it although I've been told
otherwise here, is that to maintain the same IAS (and thus dynamic pressure)
at a higher altitude, you need more power.

X, I hate to sound discouraging, but you may not find an answer here.I
looked on two websites and referenced the book Aerodynamics for naval
aviators, and they kinda contradicted each other.I think you are
looking for a real world answer to a hypothetical situation.The IAS or
dynamic pressure on a plane WILL decrease with altitude.Take a look at
a typical plane doing 300 KIAS at 10 thousand.The TAS will be within
about 40 KTS of this.Now climb up to FL350 and the KIAS will be about
230 with a TAS of about 475 (Roughly). Now you do need more power but
the point about IAS is mute (Or hypothetical) because you cant
indicate 300 KTS at 350.The part about maintaining the same AOA isnt
gonna happen either.I hope someone can explain this better.