GREAT NEWS!!! I have successfully been able to reinstall Windows 7 as 32-bit. After installing the system updates (they took forever to download), the
very first piece of software I installed was Kies mini. I downloaded a new copy of it, installed and rebooted.
Kies mini said that it was verifying updates, and after a UAC prompt, it downloaded the newest version of Kies mini. It took a while, and after it finished, I rebooted the computer, just to be safe.
I nervously waited for Windows to finish loading, and then opened Kies mini. It opened and prompted me to connect my phone. I did so, selecting Kies (firmware update), and three drivers installed successfully. Kies mini did not do anything for a few seconds after that, but then...
Voila! The famous "Unregistered device" screen with the grayed-out "Phone upgrade" button appeared! I was so happy! I went to menu and clicked "Install driver" after disconnecting my phone. It actually reinstalled two drivers, but the "Install driver" option was still there after doing so.
But that had no effect on my ability to have Kies mini finally see the phone. I tried it multiple times, and had a 100% success rate so far.
I will continue installing the other software that I need, and see if that changes anything. If something goes bonkers and makes Kies mini suddenly go blind again, I'll blame it on that software. Otherwise, I"ll blame it on myself on my failure to completely uninstall the drivers before installing Kies mini for the first time.
I'm so glad that this has worked out! Now I am soooo ready for the Gingerbread update, whenever it arrives!