You can have POP and IMAP accounts for the same email address at the same time as long as they use different mail servers. Gmail uses different mail servers for POP and IMAP. You can transparently upload mail from a POP account to a IMAP account by copying/moving it.
You can import mail from mbox files (what POP accounts use to store mail - for example "inbox." for the inbox folder and "sent items." for the sent items folder) using the ImportExportTools NG add-on. So while it would be easiest to reuse your old profile if you have problems doing that you could create/use a new one, add the desired IMAP accounts, import the mail from the other profiles POP accounts into Local Folders using the add-on, and then copy the imported messages into the appropriate IMAP account.
http://kb.mozillazine.org/Importing_folders documents how to use the older version of the ImportExportTools add-on (no NG in the name) but the basics haven't changed. Your contacts were moved from *.mab files into a abook.sqlite file in version 78 which you should be able to copy and reuse.
I suggest you experiment with some of the ideas above and then let me know exactly what you want help on.
http://kb.mozillazine.org/Posting_a_scr ... _the_forum