Win7 keys are edition specific, so a home premium key will work only with home premium and no other edition. Keys are not architecture specific so the same key will work on 32 bit windows or 64 bit for a given edition. You need to buy a win7 home premium key- the cheapest option would be a System builder edition from newegg and the like.
You dont need to do a fresh install- just enter the key via the system properties page.
FYI, system builder copies are tied to the first motherboard they are installed on and are not legally transferrable. If you want the convenience of transferrability (but using on only one computer at a given time), buy a retail copy. A retail upgrade (different from retail) is a good cheap option but since you have everything setup, it may not be a very good option. But if you're game for reinstalling the OS and everything else, Upgrade license makes sense.