Not sure if I misunderstood but moving from 32bit to 64bit is actually classed as upgrading, lol. Not the answer you were looking for but it would also have to be a clean install, regardless.
I know that windows 7 keys will work on either 32 or 64 bit regardless of what it says on the package. But I don't know how to go about downgrading ultimate to home premium, but maybe it's possible. Clean install would be better anyway though because you're better off running 64 bit.