@Smithy ****
Okay.. provided you still have the original translated and MoFA certified version of your marriage certificate.. then that's what you need to present to the District Amphur to register the marriage.. they'll usually want to see the English version as well, passport, Thai ID card, blue book for your marital home etc.. and you normally have to take a neighbour in with you to sign as a witness.. to attest to you being resident at the stated address.. and they will issue the Kor Ror 22 that you need to apply for a non-o immigrant visa based on marriage.. but would advise you to apply for the initial non-o visa at the Thai Embassy in the U.S.. which gives you a 90-day visa that can be extended in country for 12 months.. it makes life much easier.. especially if your wife needs to open a Thai Bank account to season funds in readiness for the extension 👍
Ps. Once you have the KR22 you can go to the Municipality and apply for a yellow book for your wife.. which will act as proof of address moving forward.. negating the need to constantly obtain certificates of residence from immigration.. eg. obtaining driving licenses or dealing with any business or organisation in Thailand.. banks, telecom co's, etc.. and once she has the yellow book she can return to the Amphur and apply for a pink ID card.. to be fully documented lol.. btw, a CoR will be needed when applying for the KR22 😉