Wow, thank you so much for going to all that trouble!
I tried to follow your instructions regarding the "Hidden sections" setting, but unfortunately that didn't help.
I do think there might be a difference in the way I upgraded the system: I installed a fresh 3.3, made some modifications (mainly a theme and a few plugins), and then attached it to the DB of the 3.1 instance we had. Then I logged into the Moodle, and the system upgraded the DB.
Do you think that could that explain the different behavior in the hidden sections?