Could you test in Firefox's Safe Mode? In Safe Mode, Firefox temporarily deactivates extensions, hardware acceleration, and some other advanced features to help you assess whether these are causing the problem. Here's how:

If Firefox is not running: Hold down the Shift key when starting Firefox.

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" button > Restart with Add-ons Disabled
• Help menu > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Any improvement? (More info: Diagnose Firefox issues using Troubleshoot Mode)

Safe mode did it! Thank you very much. Now I will need to go through all my extensions and other aspects of Firefox in order to identify the culprit, a daunting task. Do you have any suggestions for where I should go if the problem turns out not to be caused by an extension?

Most issues with the Options page are caused by "full" themes, older add-ons that comprehensively modified Firefox's interface. However, that usually wouldn't be limited to the Sync panel. ??