Howard Miller

That doesn't really explain to me how you migrated the database. MySQL is notoriously difficult when migrating data. The only reliable way I have found is to take a full SQL dump and then re-upload on the new server.

Almost certainly, your database is incomplete in some way.

Please tell us (in detail) how you migrated the database? Also, what's the versions of software at either end?

You can't. It would take a custom plugin of some description.

I guess it's possible to develop a plugin that checks how much a user has uploaded and overrides their permissions when it hits a limit. I can think of more than one way to approach that... but all ways would require custom development. An unsual request

Start by purging your caches (from the command line)

See Administration_via_command_line