So, I wanted to test something at work using IE7 as a standalone app since you can't have multiple versions of it running in Windows (we'll get to this later). I had previously been using IE7 Standalone on Windows XP and loved it. I had no idea it would hose some file registrations in Windows 7.
Luckily for me, there was an exact post/article that led me to a fix. Thanks pyrocam.com!
I did run into a few hangups while running through the registration batch file, having to kill regsvr32.exe a few times, but who cares. I can now go back into explorer.exe and right-click Computer.