Another quick test: Try to fill up RAM: when you boot into 1.3 (i.e., just copy a bunch of files there).
The 3000 puts its SuperKickstart image into regular fast RAM (unlike the 1000 which has dedicated RAM for storing the Kickstart). Even though 1.3 appears to be working, it might simply be because the system isn't putting enough stuff into RAM to hit the "bad" sector. Under 2.0, in addition to a Kickstart that's double the size of 1.3, there's also the copying of ENVARC: to ENV: which doesn't happen under 1.3, plus more use of T:, etc. There's a lot more use of RAM (and the RAM disk), meaning the system is more likely to hit the bad sector.
Filling up RAM: under 1.3 might achieve the same result, helping to narrow down whether you're dealing with a RAM problem or a problem with another chip.