Well, it appears ollopa was right on the money - it took me some time to get back to it, but I reflowed and reinspected the chip, reconnected the card and cables, and it read as a 7300 with the correct options! I've also removed the fan controller/touchscreen controller board and basically just wiggled the touchscreen flex connector and the screen calibrates again. I will be applying some hot glue to some connectors internally, and will need to test a couple more times, then put the top back on and shake it around good and test again, but it appears my problems have been solved.
I've seen other intermittent faults with contacts and whatnot on these scopes before (this one even wouldn't boot until the RAM was reseated), but I wonder if this unit was dropped or something - it seems like quite a few contacts were slightly ajar and I don't see any signs of corrosion or a humid environment or something.
As for the incomplete EEPROM dump, I used the onewireProxy sketch, but had modified the read function to use Serial.print instead of Serial.write, since it allowed for me to define the output over serial as hex instead of just as a character, and I wonder if the timing of returning two characters through that interface messed with the timing of reading from the onewire interface. I doubt it was significant delay in the reading of it from the MCU's side just because the functions seem to only read until the dump is complete, and since the bit-banging of the Arduino's onewire interface is already going to be substantially lower data rate than the EEPROM is capable of. I reworked the sketch to instead do two separate operations - one reading everything into an array, and then a second returning it all to the serial port - so if that was the problem, it would be worked around (and the original sketch appears to be written for absolutely minimum hardware, so there's plenty of memory available), but since I didn't have to remove it to inspect it, haven't tried the new variant.
I'd rather not keep the top off for too many more days, but if it would be helpful to try and get a complete 512 byte dump of the EEPROM, now confirmed working, let me know and I'll try and make a complete copy.