Perhaps read this https://support.mozilla.org/en-US/kb/thunderbird-and-gmail

Especially https://support.mozilla.org/en-US/kb/thunderbird-and-gmail#w_gmails-particularities

Thanks for the reply but I am not sure if you understood the question.

I have worked out how to achieve my goal using only Thunderbird.

In Thunderbird I create a folder within the GMail account called stagingpost. I find all the emails using quick filter or whatever and have them selected. I move them to staging post which really is just removing the inbox label and adding a stagingpost label. I copy all the emails in stagingpost to the local folder. I delete all the emails in stagingpost and empty bin/trash as and when.

Now I have the messages "backed up" locally.

I have tested this in a new Thunderbird profile with a GMail account with under 100 messsages. I would love someone to test this method as I need to perform it on two family members' GMail accounts who are running out of storage and have 20 and 30 thousands messages in their All Mail folder.