Savannakhet issues multiple entry Non-O based on being married to a Thai. Requirements are almost the same, but now you need to have funds of 400K baht in a Thai bank account, otherwise, they would issue a single entry Non-O visa instead.
, You may not be able to apply for an Elite visa inside Thailand or a tourist visa at some of the Thai Embassies/consulates in SEA, especially in Malaysia.
(there could be an issue when you travel to other countries that check your overstay history in any countries... not a Thai visa related though)
Your stamp should be until April 13, not April 14 if you entered on March 15 on visa exempt. Check your stamp carefully and immediately again when you apply and get your extension in your passport.
Q. I would like to know which of the two offices can I go to carry out this procedure?
-> You can apply for a tourism extension at either office.
Q. What documents do I need to bring?
-> Attached is the general information on tourism extension. AFAIK, the Chiang Mai office doesn't require more documents than listed.
Q. Also, the owner of my Airbnb accommodation told me that I don't need the TM30 and that I simply need to provide my temporary residence address during the application. Is it correct?
-> If I remember right, and if there was no recent change, CM is rather strict about TM30. You need to have a TM30 receipt (or at least TM30 registration on the system). You can try applying for an extension using a contract with your accommodation first if you want. They don't accept your application if your documents are not enough. You don't have to pay the fee in that case, just spend your time.