First, I desoldered one leg on each of the two crystals to stop the clocks. Found a 20 way test clip. Adjusted the 5V supply so it was at 5V on a logic chip. Connected the ground clip of the ABI, and tested every logic chip, marking each one with a pencil as I went.
The process took under two hours, it would probably have been quicker if I weren't restricted to the 2x16 character display, which scrolls to list the state of each pin on failure.
All the shift registers failed, but I figured the ABI must have difficulty testing these when some of the inputs are hard wired high or low, and they were unlikely to be part of the sync circuitry. The only other failure was a 74LS21 on the bottom board.
Soldering the crystals back, I looked at the two outputs of this chip on the scope, both were low. Next, I found a new 74LS21 and bent up the two output pins slightly so they wouldn't touch anything when piggybacked on the chip in circuit. The outputs of this chip had a 15khz signal, so I replaced the chip.
Starting back up, I could now see it run through the ROM based test, then coming to a stop at the screen showing all ROM and RAM OK. The test switch dipswitch was on !, which should have occured to me from the start. Anyway, it is now fully working.
In conclusion, I was able to fix a game without too much brainwork, although the process was a bit tedious. Luckily, A.S.O. didn't have any big custom chips and not too many logic chips.