@Demy *****
My opinion is simple: You came in on a tourist visa, and you should be able to use whatever immigration office that's close to you. If you and your partner are in Si Sa Ket, and they have an immigration office there, use that office. If you're in Bangkok, use MTT. If you're in [insert city here], use [insert immigration office here].
Don't make it too hard on yourself; you're stressed right now, and traveling isn't something you should want to do a lot of.