I use Listen audiobook player with a fifteen minute sleep timer. Before the sleep timer stops it playing it plays a series of soft beeps, if the phone detects any movement it will resume for another fifteen minutes.

Yes, there's still a little rewinding to do to work out where you left off but it only takes a few seconds.

https://play.google.com/store/apps/details?id=com.acmeandroi...

Two fit bits, with a recorded stop time for each of you (offset a little bit so that the part immediately before you went to sleep is repeated). When you wake up, the segment in between the two stop times has already been extracted and sent to whoever fell asleep first so that they can catch up before jointly continuing the podcast with their partner before bed.