I would create a new field called Assigned to, select or multiselect. Let's say single select as it will be easier to explain.
In the import file assign these records to a person - to make sure that it matches correctly use user ID from Epesi as a value in this field, like:
User ID 1 = Joe Doe -> use 1
User ID 23 = Some Other User -> use 23
and so on. If you want you can create an intermediate table matching User ID with users, but this is just convenience.
In Data Import module you should be able to preview how data will be imported. Most likely you will have to do it by trial and error (as is the case in most data migration situation), therefore make sure to create a backup before importing data or any serious database modification. Ideally create a clone of a production Epesi instance for testing purposes and try import into this testing/development instance first.
The other approach is to go directly into the database via tools like phpMyAdmin and update records there. You can also write a patch in PHP that would update your records, but this would be worth exploring if you perform this kind of data import on a regular basis and would like to automate it.
Do you use some logical criteria (like for example salesperson responsible for certain territory like a state or a city), that you could create some update SQL query or queries? If yes then import everything in bulk and then use SQL tool to update records.