Thanks for the update!
There's nothing obvious in the logs. You seem to be using a Hifiberry DAC, in which case the clocks are generated by the RPi. Therefore my best guess now is the RPi kernel PCM clock patch in combination with the way mpd uses alsa.
In order to track down the issue I'll need to be able to reproduce this locally, so I'll need some more information and detailed step how to reproduce this:
set log_level=verbose in mpd.conf, reboot the RPi, then try to trigger the issue.
After that post the mpd log, output of "journalctl -a | paste" and your config.txt and mpd.conf files.
It could be related to the file played (or the file played immediately before that), so having the "mediainfo" output of these files would also help.
so long,
Hias