I would recomend you get a linux box with mysql. ODBC access from your winbox to your local linux box. Open your dvd access file and your access file which has tables ODBC linked to myslq. Use copy paste to transfer data, access is really good at that. Once you have all the data transfered close files and turn your atention to the linux box. Use mysqldump to create a dbase dump. FTP the file to your server and import from local file.
I had the same problems you did, specially with text fields. The use of Accesse's native copy paste is great.
Saludos
Gerardo