IIRC if you do a clean install of windows 7, then upgrade on top of that with the media creation tool, will upgrade to the same version. So, clean install with media for the version you want, you have, activate, run the media creation tool to upgrade the system (and I chose to keep nothing), then pick the appropriate 64 bit version.
If you lack media https://www.microsoft.com/en-au/software-download/home will get you the exact version in either bitness you have based on the key. I actually lost my key, and windows 7 had some issues with the strange partition setup I had, so I ended up using produkey to recovery my installation key. With the next milestone, you should be able to use your old key directly to reinstall, but with modern install times, and a clean install,its 10 minutes or so. You can download 64 bit media here and it will work with a 32 bit key. Might be worth it for a less painful upgrade.
All it seems to do is check if your windows system is activated, so it should just work. I'd note, there's a specific error if a system's not activated correctly. Media creation tool dosen't seem to check if a key was used before, and well, for OEM boxes the key's the same for many boxen anyway.
Also, the 'free upgrade offer' is dependent on an update. Its not actually dependent on eligibility. I sort of groggily used the wrong media, assumed the key was in place, ran the upgrade tool and well, it failed. I might be wrong though, and lacked caffeine at the time but you can use the creation tool at any time, at almost any update level.