No Bluetooth Audio with Ford Sync

I had a problem crop up yesterday with my iPhone and Ford Sync.

While my iPhone pairs up as always and the phone functions work as expected, when I try to switch to Bluetooth Audio as a source, Sync says no bluetooth device is connected, and it is unable to connect one when it tries. (This is in spite of the fact that there IS a bluetooth connection indicated, and the phone functions work fine.)

Even since I have been using an iPhone with my Sync system, it has seemed that the phone is somehow being interpreted as two separate devices - one that functions as the "phone," and one that functions as the audio source (for listening to music, podcasts, etc.) So it is as if the one that did the audio stream is not being found, but the other one is working fine.

Yesterday, I was able to get Sync to recognize (or say that it did) the bluetooth audio device. However, during these times, no audio would actually play through the system, even though the phone indicated that audio was playing.

So far, I have tried all of the remedies I've seen online for other Sync/iOS7 related trouble, including resetting and restoring the phone, and deleting the stored bluetooth connection information from both the Sync system and the phone and reestablishing the connection. Nothing has had any effect on the problem though. I'm wondering if there is anything else I can try, as this was a wonderful setup before this update.