If all you've got is table data and you can access the MySQL server from your computer, then all you have to do is export it from Access:
1) Install MyODBC (the ODBC driver for MySQL)
2) Create an ODBC connection for the host's MySQL server.
3) Open your mdb files in Access.
4) Highlight the table you want to transfer to MySQL and choose File -> Export.
5) In the "Save as type" dropdown, select "ODBC Databases()" - it's probably the last item in the dropdown.
6) Select your MySQL ODBC entery.
Although I've never used MySQL, that should work in theory. The only hangup would be if your host doesn't allow everyone in the world (the internet) to see the IP of the MySQL server (which is certainly possible).
err...I just reread the post, and I realize that you've already done some of what I said. You should be able to start at step #3 in the instructions above and everything should work fine.
Hope that helps,