Welp, AVG embeds itself on the level of a virus.
First, I started ripping out every AVG registry item I could. I cleaned out plenty of stuff with that. I also disabled a couple of services. After spending at least an hour picking out various registries and repeatedly trying to run File Shredder to destroy it, I called upon CCleaner to help me. I took out so much stuff that CCleaner counted it as uninstalled and removed the last of the registries for me. I also used it to remove the shell extension, a bunch of "add-ons" for Internet Explorer, things like that. Then I'm at where I am right now. What's worse is that it's STILL running in SOMETHING so File Shredder can't delete it.