Update ...
Sent my phone in to the admin who's responsible for them. I included a full page of handwritten notes on what it does and what I had tried to do to correct it (different batteries, wipe handheld, and firmware update). In my message, I also asked her to please be sure to remove the battery if sending it interoffice mail, so that it wouldn't be making calls from the envelope AGAIN.
So, of course, I got a hand-written note back with the same phone saying "couldn't find anything wrong."
Ended up going directly to the phone vendor who replaced it immediately.
Been happy with the replacement for about 72 hrs ... fingers crossed it will stay good!