Update on the situation:
I went ahead and captured the zenith power generator, for several reasons. One is that capturing it didn't put the homeworld on alert, just the world bordering it. Two is that the border world on alert had five data centers, a huge find at this late stage in the game. I was lucky enough to find raptors in an ARS some time back, and had no idea how effective they were at infrastructure raiding until I landed my fleet on the border planet with a full complement of MKI through IV raptors. I expected a long slog to clear out all the guard posts and data centers, only to watch in dumbfounded amazement as the raptors took out four of the data centers and eight of the ten guard posts in one run. Because I'm relying almost entirely on Z generators my economy is in crazy good shape, and within ten minutes I was able to clear out the rest of them with no problem.
With the border world fully neutered and both Core homeworlds scouted, I currently own 12 planets, and my AIP sits at 120.
After completion I'll post the full log in the AAR section.