My problem is:
For years I've been using Gmail + POP3 to Thunderbird -
the mail is organised in Thunderbird - and is *not* organised in Gmail
So, in order to change anything, I'll have to organise all that stuff in gmail....
I could be wrong so back things up first, but...
I think if you switch the settings in GMail to use IMAP, and then change the server settings in TBird to use the GMail IMAP servers, your folder hierarchy and existing message store should be preserved and replicate back up to GMail.
Alternatively, you could create a "new" account using the IMAP settings in TBird, and then just move the folders in the old TBird POP account into it. (Again you'll want to have a backup made first.)
IIRC, when I switched my GMail accounts from POP to use IMAP I didn't need to rearrange or do anything. Because prior to the change, all my custom folders were local anyway.
The only thing that might trip you up are the storage limits if you're one of those people who keep everything (especially huge PDFs and other enclosures) in your email app and use it as a filing cabinet