I FOUND THE FIX!
Don't ask me why this could ever work, but it does. I couldn't replicate the successful sync booting normally, or when I deliberately went into safe mode. But as I was thinking about that one weird safe mode boot, I remembered that the screen was tiny and the colors were all off, so I started playing around with the display settings. I set the display resolution to 800x600 from inside the Windows display settings, but couldn't figure out how to manually adjust color settings. So I just saved it all at 800x600 and opened up iTunes. iTunes gave me a message complaining that the screen was too small, but I closed it and iTunes opened anyway. There were areas of the UI that were cut off, but when I hit the sync button, it went off without a hitch.
So after three days of messing around with USB drivers, user permissions, and software updates, the problem was solved by changing the resolution of my imaginary screen. Computers are extremely weird.