I won! At last, lol. I followed the advice here and took out the harder AI first (Vanilla with those Teuthida drones, ugh), so the second seemed like a cakewalk. The second AI was a level-4 Tank with a Raid Engine Guard Post, a Fortress, and a few other things. It still took me 3 or 4 raids to kill it, but each raid achieved something constructive, unlike my comical efforts against the Vanilla AI.
Also, I took another piece of advice I see a lot here: I used Transports to attack the Homeworld, from 3 hops away. Wow, I wish I'd tried these earlier. I packed up three of them, and was happy to see that even starships fit inside. (Some big Spire ships did not, though, so I left them behind.) The transports zipped through the two intervening systems so fast that I was at the Core-World target before I knew it!
If I had to level a criticism at my own gameplay, I'd say I'm waaay too slow. It took me 24 hours to finish this 60-planet map. And yet I took only 14 planets! That's barely more than a planet every two hours, whereas x4000 says he takes one every 45 minutes. My cautious nature is my undoing.
Also, 14 planets might have been a bit too conservative; I was probably unduly hyper about my AIP, which ended at 417, after killing the second homeworld. At this difficulty level, I was never close to getting to AIP(III), which wouldn't have kicked in til 700 or so. I could have used the extra knowledge and crystal/metal. Metal/crystal was a problem the entire game, what with all those fabricators and starships building (and the occasional merc ship and Trader-bought goodie). I amassed only 53,000 knowledge. Could've used more.
My raw score was 3.2 million; adjusted score only 91,406, lower than one of my losses on Defender mode! (I took a hit for difficulty level, for using Easy Broken Golems, and other things.)
Anyway, thanks for all the help in this thread. Now the question is: what next? I'm thinking 7/7, as this did feel too easy, except for the epic fight for the first Homeworld. I have all 4 expansions; I might want to enable Complex ships (had Normal this time). But I'm also interested in trying the Spire campaign. Is that a good challenge?