Questions: What would cause the huge power swings from one turn to another?
Bankruptcy is just about the only thing which pushes the AI's global settings around aggressively. Money production is, for some reason, hugely overrated in power score terms (while money on-hand isn't). So if they ran out of cash for maintenance, hit their spend-til-broke limit, and then had to go 100% econ for a turn or two, that's cause big swings in power score from turn to turn.
Check their econoic power graph; if it's very 'spikey' then they're stuck in a bankruptcy cycle where they run out of cash, go 100% econ, then have enough cash to go back to normal spending for 1-2 turns, bankrupt again, and continue like this until their losses go down.
Shouldn't there have been a few successful invasions?
I don't know if this has changed for 1.3, but in 1.2 the AI only has an invasion range of about 16 tiles.
Can the AI ever win a conquest victory on an Insane map?
Hahahahahahaahahhahahahahahahaahahahahahaha. Good one.
Oh, you're serious?!?
No. No chance. Not in a million years of soaks.
The scripts are timed wrong. It thinks the opening 30 turns are the 'colony rush'. After that, it diversifies a lot and it's colonization rate goes off a cliff. I didn't want to re-write the AI scripts completely for IAB. I had to rewrite them from scratch. The scripts are basically best-guesses at what the AI ought to be doing at turn X. There is an enormous difference between what it should be doing on turn X on a small map to what it should be doing on an insane map. This is completely unaccounted for in the triggers, and so the AI does the same thing regardless.
As I say, I've not been banging on about the AI scripts being kind of high priority for no good reason. The enormous difference in scale between a tiny map and an immense or insane one requires the AI to think on entirely different time scales, and there's presently no way to tell it to do so.