What is the process for re-entering Thailand with an existing visa if I'm obtaining a new passport in my home country?

Brett South the easiest way to do it, and you have plenty of time if you are here until February next year, is to apply for, and get, your new passport while you are in Thailand. After you get your new one you simply go to immigration with both, and get your extension transferred to your new passport while you are here. It's done online.

Brett South you need the re-entry permit before leaving, or your current visa/extension becomes invalid the moment you get stamped out of Thailand.

The re-emtry pernit is valid for the duration of your existing visa/extension.

That means if you come back after that date, your visa/will be expired, along with the re-entry permit, and you will need to start over.

If you come back before that date, you just show both passports. Old one with the visa/extension + re-entry permit, and new one.

They will stamp you in on your new passport, and make a note in it referring your old passport.

You then take both passports to immigration inside Thailand, to get your stamp from there transfered over to the new passport.

But, as said, if you don't come back before your existing visa/extension expires, then you lose that regardless.