Hmm. Would a 512k with Plus ROMs still be limited to System 6.0.2?
I'll give it one more go with a lower System.
A 512K with Mac Plus ROMs makes it a 512Ke. Memory permitting, you can have it run from system 3.2/Finder 4.0 to 7.1. System 7.1 will not run on a 512Ke unless you expanded the RAM with an extra RAM Card like the Dove Board. I used to have System 7 on a 512Ke with a 2MB Dove Board, giving the Mac 2.5MB!
Otherwise, you can run up to System 6.08 on a Mac 512K provided the system is trimmed down to fit into RAM.
Somewhere I have a System 1.0 disk, and it won't run on a 512Ke or Plus, it always crashes on Boot- Happy Mac and then Sad Mac. It will run on a 512K and 128K with the older ROMs.
Somewhere I remember, anything before System 3.2/Finder 4.0, you need the disk (floppy or hard drive) to be formatted in MFS and not HFS, or else it will also crash on Boot.