I was encountering this same issue on Gentoo. It appeared to be at random times but persistent once it started. I realized that it only happens if 'gnome-control-center bluetooth' is open. I would often leave this open after pairing the device, not really thinking about it. As soon as I close it the "module-bluez5-device.c: Skipping..." messages stop and the choppy sound goes away.
I was encountering this same issue on Gentoo. It appeared to be at random times but persistent once it started. I realized that it only happens if 'gnome- control- center bluetooth' is open. I would often leave this open after pairing the device, not really thinking about it. As soon as I close it the "module- bluez5- device. c: Skipping..." messages stop and the choppy sound goes away.
Posting in case it helps track this down.