Export/import portal users - names not preserved (or exported), only email address -- can't match to imported ownership

I am trying to transfer data to a new application. When I export portal users only the email address is exported. When I import them in the target portal, the name that is associated with the user does not match the name in the original portal. Unfortunately, record ownership (Added_User) is by name, which means it is impossible by any means I'm aware of to match the ownership of the imported records to the correct user.

Is there a way to control the name of the user on imported portal users? Is there a way to match ownership of imported records to the correct user when importing? I know I need to use a proxy field to track ownership in place of the Added_User field, the issue is in figuring out the value to put into that field since for many of my records the name in the exported data does not exist in the list of names for the imported users.