Avast support came through for me. They told me to reinstall the standalone version of Secureline, using Administrative privileges, so I did that.
I reinstalled without first removing anything. When I opened Secureline, it connected immediately. I had to login to my account to recognize my license, but that also worked, although the app did have to reconnect apparently. But it worked. So it works again, and this is sure easier than uninstalling Premier first! Especially since I would have to redownload the latest version...