I you dont mind, Im going to resurrect this thread to assist others finding a solution.
I have the same issues as OP, my ONE M8 (stock android 6.0) started ringing this afternoon, and when i picked up the phone, there was no prompt to answer the phone, in fact, there was no app icon (ie music) running at all. The ringtones would often come in groups , layering over the top of each other till the sound was a complete mess. When you dial a number during the ringtone playing, the ringtone stops for a second, then starts playing through the speakers, but making calls is possible , as is receiving calls. I also noted the car app turning up in recently used even though it is not being activated. The ringtones seem to be as random as but approximately 20ish rings an hour.
I changed ringtone and the phantom rings also changed, confirming it wasnt a random alarm.
I soft reset the phone numerous times to no avail.
I disabled many apps, including the Car app, Skype, and twitter, no result.
I restarted in safe mode as mentioned above, no change.
I deleted cache partition, no change.
I guess im going to reset to factory, but I can think of better things to do with my evening