@Orb
Based on the info you have given, my diagnosis is that the floppy drive in the A600 is not entirely compatible with the floppy drive of the A500. They probably installed the same kind of lame drive that caused all the problems on the A1200.
I think that's unlikely, otherwise we'd have heard a lot more about it in 1992. The 1200's floppy issues didn't appear until the Escom era. Of course, if that 600 has had it's floppy replaced during its lifespan, there's that possibility.
I think it could still be a kickstart issue. The 500 probably has 37.175 and the 600 probably has 37.300 or 37.350. There could be subtle changes between both of those 2.0 chips that cause 1.3-era stuff to fail. Orb, can you softkick 1.3? Try SKick on Aminet.
