I wonder if there's a way to do a data Export from Access.

If it can export 1 or 2 databases into an easy-to-read sql file then...

(thinking out loud) you could possibly massage the commands so that the same
data dump can be imported into a MYSQL GUI front-end such as PHPMyAdmin.

If this can be done, you'd have to first freeze the app so that no new data is
collected on the MS side after the export process.