Is there a way to actually uninstall all of GSX so that I can start over?
If you reply YES to the question "Do you want to remove the Addon Manager ?", it's almost a clean uninstall.
There always seems to be something left, like the serial numbers.
That's something we NEVER do, not even with the complete uninstall: we don't want have users risking losing their activation, just because they uninstall it. But a Serial Number won't stay in the registry, unless it passed the activation.
It's not possible to end up with a "wrong" Serial number in the registry, unless you place it on purpose, by manually editing the registry.