I would just install AVG after uninstalling Norton. Having AVG and Norton running just to install Norton probably isn't going to be much worse than just being "wide open" for a few minutes. The thing with Norton is that it helps prevent viruses, so you should be relatively clean.
If you want to have your system as norton free as possible, I would probably do the regular uninstall, reboot, then run CCleaner's registry cleaner 2-3 times. It should get about everything. ccleaner -
http://filehippo.com - And you can get the new beta, or the last stable version.