Final idea:

Go to about:support again and click the button near the top to "Refresh Firefox." Usually you get that prompt if it's been a long time since you've opened Firefox. What it actually does is create a new profile for you behind the scenes and migrate all your data to it. It could somehow fix something along the way. It's a bit less obnoxious than creating a new profile since your history will be carried along, but I guess it's possible the thing that is causing a problem might also be "refreshed" into the new profile.