I also tried un/re pair and the results were the same - call connectivity only, no media after the initial pwiring. Its almost like the media connection expiers after 24 hours. I think the un/re correction may have more to do with the individual BT devices, though I am not 100% certain. The data wipe method works every time, its just cumbersome and frustrating....
Someone in another thread suggested a battery pull after turning off the wifi, then starting it up again and repairing, which did end up working for me. The update was causing several issues, especially with Bluetooth, before I tried that. So far, so good, since then.
I am also having an issue with Bluetooth connectivity for media on my LG G3. The phone went really strange last week when the numbers on the unlock screen number pad (phone was encrypted) kept rearranging themselves in random order. While the Phone worked, I still decided to to a factory restore. That went fine, and the phone has seemed normal, till today when I tried to connect to my Nissan Murano for media playback. Bluetooth hands free phone connection is fine, but it just never makes a Bluetooth media connection to the car. When I then tried the LG G3 with a previously used Bluetooth headset, I got the same result. For a test, i was able to pair that headset with other devices, and the car with a Samsung tablet, just like always, and without any problems or delays.
Unlike some, my wireless is fine, it just will not connect through Bluetooth to any media device. I have been using the same phone/headset/car connections for over two years and never had an issue. Given this wave of problems, I have to say this really seems like a deliberate crippling of the LG G3, to move people onto new phones. While I may change phones, I won't do it on Verizon.