Thank you all for the suggestions. The comment about thumbnailing gave me some hope, as it makes sense that the thumbnails would be rebuilding after installing MC24 from scratch and restoring the library. But despite lowering thumbnail priority from medium to low, there are still one or two dropouts on every track played. I have also noticed this: if I interact with MC24 (e.g., skip or rate tracks, modify playlists), be it through the Win10 client or via VNC, the frequency of dropouts increases. If I leave everything alone, it goes back down to one or two per track.
I hadn't considered updating Raspian to Stretch, but that may be my next step. Just out of curiosity, erviv, did you start from a fresh install of Stretch, or did you dist-upgrade Jessie? I've been hesitant to upgrade given the warnings of possible failures.