Media Monkey uses SQLite as database. I have used Media monkey to, before I switched to Linux. So I extracted the last played timestamp and play count with a simple SQL select and migrated this info to strawberry, which uses also SQLite. But be aware that both stores the date in an incompatible way. It’s not that easy to spot in Media monkey database.
You can also use a Windows program like Media Monkey or Musicbee on Linux through Wine. So you don’t have to migrate your database. Syncing will work for both with Media Monkey and Musicbee.