Thanks for the replies guys.
I've actually just added each account using the new Dreamhost settings and then copy over all the emails from the old GoDaddy Inbox to the Dreamhost Inbox and it is populating the server accordingly using IMAP. Seems to be working for INBOX, SENT and DELETED emails correctly. It's just taking some time for the larger emails for a few users.
This method seems much simpler, it should work, right, or am I missing something important?