It is definitely possible to synchronise offline mail in Thunderbird using IMAP. I am doing just this, for both a Google account and another IMAP account. Using IMAP (in my opinion) is preferable to POP3, because I can make changes locally and they get reflected in the webmail server and then also on other machines I have Thunderbird running on.
I don't remember the exact steps, but setting up the Google account was different. There is a different wizard for it that makes it easier, and this also provided some settings for me. It sounds like you've been able to get Gmail working in Thunderbird over IMAP - so you must have found this wizard.
I have a number of custom folders, so I had to do this for each of the ones I was interested in. Right-click on the folder, and go to Properties. I had to check the "When getting new messages for this account, always check this folder" option to ensure I got notifications properly - sometimes I would miss seeing new e-mails in custom folders.
Then under Synchronization:
It can take some time to download all the messages, but I am able to access them offline.
The only difference with your setup and mine is I have set to store all e-mail. I don't know how the above "Select this folder for offline use" will correspond with the 90 days setting you have globally for the account.