@SimonUrbanek Thanks!
It works now.
Long story short: Yes, I had tried multiple times, stopping and restarting the app, waited what I thought was a reasonable time after installing the lockscreen widget, no luck. (But the non-premium lockscreen widgets worked just fine.) After I read your message, I tried a regular (non-lockscreen) premium widget, and it worked fine. Went back and tried the lockscreen widget once more, and it worked right away. So I never needed to try the big uninstall/restart/reinstall song and dance. And of course, I have no idea why it didn't work before, nor whether anything I tried helped. Maybe the problem just decided to fix itself.