Animan99 was nice enough to send me an Angus chip for testing.
Sadly, I am still getting the green screen with this chip in place of my MegaChip.
I also took a photo of my 68000 socket after my cleaning job, though the image could be a bit clearer.

I still think it would be best to ship the mother board to someone who could perhaps put a new socket in place for the 68000, as well as repair any damage that the battery might have done to the circuit board.
The seller said it was booting up before he shipped it, and I was able to get it to boot up a few times after I cleaned it.
The fact that I changed nothing, and it is now back to booting up to the green screen, tells me that even if I do get it to boot again, I'll be dealing with a very unstable system.
Anyone up for the task within the U.S.?