Did you try to revert back to 1.08 and keep the 3.41 bluetooth folder and see if bluetooth worked?
Here's the steps I've done so far. I reverted back to 1.08, then using the 1.03 firmware while in 1.08 I updated the bluetooth. So while the radio is in the 1.08 firmware it successfully updated to 3.41.10. I tested bluetooth audio and calling, and everything is working great.
I then updated to 1.03 again. The 3.41.10 bluetooth firmware stayed put. The radio actually ran much more reliably. The first time carplay was utterly unusable and glitchy and half the buttons on the radio weren't cooperating. This time though the radio responded fine and carplay moved fine. The only problem was the same problem. The bluetooth audio would not switch from off to on.
So I tried something crazy. I thought "hey what if the recovery is on the device side? So when you install an update it installs a recovery update as well so if your flash drive dies the radio fixes itself." So I tried the crazy plan. I turned off my radio during the downgrade from 1.08 to 1.03.
Yep I went full nuts. I now know how the restore process works. It works from the SD card, not from the Radio. It used the 1.08 update file to do a restore install. Interestingly it did NOT revert me back to the 3.21.10 bluetooth firmware.
So there you have it. My current findings.