Loots like I had more spares than I thought. I swapped the CPU, CIAs, Kickstart, Gary, Agnus (an 8370 for the 8371), Paula and Denise. Of course, I can't speak to whether the spares were also dead, but I took my chances. (This is an A1500, btw, but it had an upgraded Denise .. the 8373!
I also discovered that the reason my keyboard light did not come on was because the keyboard light in that keyboard was dead. Everything else about it was fine. :/
Under the cpu actually looks better than the areas to either side of it, which have a bit of the grunge from the battery leak. The underside of the board is entirely pristine.
My next job will be to measure resisters, put some capacitors in the problem area on order for replacement, and use the R6 schematic, as best I can, to check all the traces coming out of the cpu.
Any other advice is welcome. Desperately welcome, in fact. I'm still especially interested in the significance of the one second blue-screen flash. Should I take that seriously?
I would look carefully around the battery area, especially around & under the CPU socket area.
But I'd start with every socketed chip - press down firmly on them, inspect their pins, etc. Also what version ROM do you have in here? Do you have a spare you could swap in? A bit scatter-brained today, just thinking out-loud of other common problems. When was the last time this system worked? Have you tried with any/all expansion cards removed and devices disconnected?
Edit: this link has lots of info on Amiga custom chips: https://en.wikipedia.org/wiki/Original_Chip_Set
and this one: https://en.wikipedia.org/wiki/Amiga_custom_chips