A quick-and-dirty way to upsize Jet/ACE tables to any ODBC-accessible database engine:
create an ODBC DSN for your database.
in Access, select a table, and choose EXPORT from the file menu. Choose ODBC as the type and then select your DSN.
This will export the table and its data with data types that your ODBC driver indicates are most compatible with Jet/ACE's data types. It won't necessarily guess right, and that's why you likely wouldn't do this with SQL Server (for which there are tools that do better translating). But with non-SQL Server databases, this can be an excellent starting place.