PMs aren’t a big deal. That’s why I suggest making a CSV for each member. Or give your members an x amount of time as a grace period before you begin the migration.
Or a combo: make the old site an archive for x amount of time for members to collect PMs. After that time has passed, nuke the site and mysql database. Be sure to add a robots.txt rule for that new archive folder so it isn’t crawled any longer. Push that google juice to the new Discourse digs. 