Well, I done screwed up. It turns out you have to manually enable autosave, so when I tried to load up an autosave to undo a strategic mistake, I wound up losing about an hour's worth of progress. Yikes.
It wasn't a total disaster, though. The save was after I built my four Dyson spheres and powerful carrier fleet, but before I got into the confrontation that lead to my fleet being destroyed by an inexplicably stronger opposition. I think the problem is that my fleet was too generalized - in addition to having top-tier weapons and armor, it also had construction and info-war facilities, and thus was less densely armed than dedicated war ships. Another explanation might be that my carriers weren't actually carrying anything, and were relying exclusively on their secondary weapons.
You know, that's probably it.
It's only somewhat my fault, though. Everything in this game takes more clicks than it ought to. To build a fighter ship for my carrier, I first have to click on the unit stack, then click on the specific carrier, then click on the build queue menu, then on the units tab, then on the fighter ship, then on a quantity button, but since the carrier can hold 16 fighters, I have to choose 15 and then 1. It's a total pain.
That being said, there's no real excuse for that. I assumed that because I was at the top of the tech tree, I would be so overwhelmingly powerful that I didn't need to take precautions. I was wrong. In a way, this lost hour is a gift. Now I can build up my forces in a reasonable way and face the aliens fully prepared.
I'm just not looking forward to all the clicking I'll have to do.