Well, if he's going to load 7.6 on it, then he'll need a 32-bit clean ROM anyway, in which case he doesn't need MODE32.
It also occurred to me that my IIci is 32-bit clean, so that's probably why it works just fine with the 128MBs of RAM.
I bet if he had a 32-bit clean ROM it'd work fine even with 7.5.5, and I'd be willing to bet the 128MBs of RAM would work with a 32-bit clean ROM, as well.
I think this is case closed.