I'm not dead certain of this, but I believe that you can use the 32 bit Windows 7 install to qualify the installation of the 64 bit version.
Boot from the X64 DVD or a prepared USB flash drive (recommended). The X64 installer will detect the pre-installed 32 bit version, and let you proceed normally with the clean install of X64 (using the upgrade license).
An irrelevant cavil: you can physically install Windows 7 on any number of PCs using the same installation disk. (I'm not sure that would be permitted under the license agreement, but I know of no enforcement of that.) You may only activate as many of those copies as your license permits (one for most, 3 for a family pack). As you can't run Windows 7 for more than 30 days (up to 120 days with the re-arm procedure) without activation, the practical difference between "install" and "activate" has little importance.