You don't even need to be in protected mode to use 32-bit registers. You can sort of bounce in and out just enough to use them with the 66 prefix. I used to do that but it's been so long I forgot how.
That's right, I was, but on further reflection you don't need to do anything special in this case since it's just doing 32 bit math, not 32 bit addressing. EAX/EBX/etc should just work in real mode IIRC.
