I downloaded the CA uninstaller and tried it myself, and yes, what you say is correct (as you know), it offers to have a CA tech take remote control of your PC.
I understand your reservation. I'd have a reservation myself, though it probably is quite kosher and OK.
(You just don't want a stranger, no matter how professional, going through your computer settings, do you?)
Anyway, it's up to you if you want to do that, there are a few things we can try first.
I'd try the Avira registry cleaner. The 7th tool
here.download it to your desktop, extract all contents to the desktop. (You'll need to use a zip program. You probably have a version of Winzip installed, which will unzip the contents of the folder for you.)
Once all are extracted, double-click the file shaped like a red and white umbrella. Select "configuration", and
un-tick the HKEY-current user" box.
Then click "scan for keys". It will take a minute or two.
There are likely to be 6 entries found for Avast. (don't touch those.)
If any are found for any other AV, please post the result here (there is no easy way to copy and paste the result, sorry, you'll have to type it out), or take a screenshot and post that, please.