Last follow-up: I got the board out of my cab and started probing on the bench. After checking all the diodes and transistors around the battery circuit, I started tracing where the battery power goes (the backup rams). No problems detected.
Looking at the MVS-1 schematic (the only one I could find anywhere on line), the system uses 2 ram chips, each 8 bits wide, one for upper, one for lower. Since the error message indicated that only one of them was bad, I wanted to figure out which one it was (so I didn't have to replace a good chip). I did this by tracing back to the 74HC32 that sources the write signals (BWU and BWL). Using a DMM, I verified that pin 27 on the one RAM chip connected to pin 8 on the HC32, but when I tried to prove that pin 27 on the other chip connected to pin 6 on HC32, it acted as if it wasn't connected.
I examined the board, trying to follow the traces and found that the trace from pin 6 goes on the bottom of the board to a via, where to jumps to the top of the board and goes to pin 27 on one of the RAMs. Further probing showed that pin 6 of the HC32 was NOT connected to the via, even though I could see the trace! Closer examination with a magnifier (and use of alcohol to remove residue from the rubber pad that was on there) finally located a slight nick in the trace, which apparently was enough to disconnect it.
I ran a wire from pin 6 of the HC32 to the via, and I was now able to prove that pin 6 ran to pin 27 of the appropriate RAM.
I suspect that the trace was damaged during previous repairs, and has been intermittent. For some reason it recently decided to give up the ghost altogether. This board had obviously been repaired before, multiple times. There was evidence of swapping of one of the custom chips (nicely done, if there wasn't a little left-over flux I'm not sure I'd have been able to tell), and the headphone jacks & volume controls had big blobs of solder on them, indicating replacement by someone less skilled (or perhaps lacking a proper iron). I cleaned up the volume related stuff just because it looked nasty, and I also removed the 470 ohm resistor and replaced the remote nicad battery pack that I had been using with a coin-cell holder on the board.
After all of that, the thing fired right up, Aero Fighters 2 worked great, as did the other game I keep in there, Bust-A-Move Again.
Definite points to the SNK engineers for making the board not impossible to work on.
Definite negative points to the SNK engineers for not putting individual chip designators on the board. It makes it hard to talk about it.
Once again, thanks for all your help.
EDIT: full log of the whole repair
http://www.kohne.org/mike'sprojects/fixing-a-neo-geo-mvs-2-slot-board-backup-memory-error