Fortunately for me, AVG's software did actually let me uninstall it -- unlike Symantec's stuff, which seems to never really get all of its tendrils out of your system unless you go back to "bare metal." I still had the version 7.5 installer on hand, and the license key for it still worked, thank goodness. After getting rid of 8.0 and reinstalling 7.5 (and the huge amount of updates for it), I was very relieved to see VPN running as before, and I was able to get back to work.
As part of the removal process with 8.0, AVG asked why I was removing it, and I explained in no uncertain terms that it was incompatible with software that must work for me. Cisco VPN may be rotten software -- it's so badly written that my registry-cleaner software keeps trying to remove it -- but it's what my company requires, so I'm stuck with it.
Now I have to hope that AVG fixes the bugs in 8.x or keeps updating 7.5 for a while longer.