Hmm, could be tricky depending on how inter-dependent things are historically, so good move having a copy of the database.
One thing you could try on your copied test server is to produce some ticketSQL that will find all the tickets for the queue(s) that the new company would have. Once you’ve got something that will select them all, use the RT shredder to remove them from the old company’s database but also save a copy of the SQL. Then use that SQL file to re-inject them into the new company’s RT instance.
However before importing the saved deleted ticket SQL you might need to ensure that you have first created the required users in the new company’s database. The tricky part will come if tickets owned by the new company involve any transactions that users staying with the old company were involved with. You might want to export all the users from the old company to the new company, then import the tickets into the new company and then use the shredder again on the new company server to remove unwanted users.
Alternatively, do it the other way round and produce ticketSQL to find all the tickets that the new company has nothing to do with, and then shred those in the new company’s RT database (starting with a copy of the old company’s RT system). Once that’s done shred RT users in the new company’s instance that are unwanted. Once you’re happy with that, you’ll still need to remove the tickets that have gone from the old company to the new company from the old company’s RT instance though (along with any users transfer to the new company).