I think I have a workable solution, using your IMAP suggestion (I found out my email server is IMAP capable).
In Thunderbird, on my desktop, I have my email set as IMAP. I started over "fresh," mostly because I realized a lot of what is taking space is attachments and there is no easy way to delete them all. I have my "local folders" that still contain the previous [multiple] years worth of email, and I'll probably make a copy to my laptop, but I'll only have to do this one time, since the IMAP will sync folders as needed (I believe). I'm not 100% sure how that works, if it is an on demand type thing or if it checks all folders every time, but it is not often that I am without an internet connection, especially when dealing with email

I'll try to get into the habit of deleting attachments, within reason, like images from clients since those would then go to their FTP sites most likely, and if the IMAP account gets too large, I'll then "archive" it to the "local folders."