I have already made a bootable USB as described, ran FRST, uninstalled Avast via a FIX file, the Avast Cleanup Tool, manual scrubbing of the System32 folder, and disable registry entry commands made via the Recovery Console. There should be no trace of Avast left, and yet, there apparently are still drivers somewhere that I cannot find.

So yes, I can boot from the USB drive and do things from there, such as copy and paste registries. But as I stated above, copying a brand-new default registry and pasting it into the \system\config folder does not fix the problem.