Well folks, I caved in and went for the factory reset . . .
I did it from my PC and then proceeded to start the whole setup process from scratch. So far everything is working fine, except that it wasted about 3 hours of my time.
The real test will be in 24 hours, if everything still works properly (last time, it worked for the first few hours and then the problems began).
A thought I had: It could be that this problem is specific to devices that get unlocked by a re-seller and then get sold to end users. The re-seller (at least in my case) had to start-up the phone and enter some kind of BBID in order to be able to unlock the phone (the first thing the BB using OS7 asks you for when starting up for the first time is your BBID). Then it seems that once the phone gets logged in with a BBID, for some reason (definetly a bug IMHO) it doesn't allow a user to change the BBID on that particular device without first wiping it or reseting to factory defaults. That means if you change your BBID, for whatever reason, you are screwed. If you sell your device, or give it to your wife/kid/friend or to a co-worker, you are screwed (although in this case you'd probably wipe it first anyway). Thus, anybody who buys an unlocked OS7 device should first make sure its reset to factory state before getting started.
Seems to me like a serious bug that RIM needs to deal with.
