I am trying to do the same! I am in the process of researching it and I'll try and get it done this month and next. I'll keep this post updated as I go through the motions, and it would be great if you do the same, with your experiences.
The big picture is as follows (as I understand it). I will go in reverse order, it actually makes more sense that way.
1/ Thai Immigration requires a KR22 (a.k.a. Kor Ror 22), in support of an EOS application based on marriage. (If you plan on doing retirement-based EOS or LTR, Thai Immigration does not need a KR22.) KR22 is not an MC - it is a document issued by your local Thai county (Amphur), certifying that you are married.
2/ In order to issue KR22, Amphur requires an MC certified by Ministry of Foreign Affairs (MFA) (I am not 100% about this part).
3/ In order to certify an MC, MFA requires an MC to be translated and certified by the Thai Consulate (or Embassy) in the US.
4/ In order to translate and certify an MC, the Thai Consulate requires the MC to be certified by the US Department of State, and Apostilled by the State where the MC was issued.
5/ In order for the DoS and State to certify/apostille the MC, the DoS and State require an original certified copy of the MC issued by the county where the marriage was registered.
Put another way, the sequence is as follows:
1/ Get an official MC at the county.
2/ Get the MC apostilled by the State.
3/ Get the MC certified by the Department of State.
4/ Get the MC translated and certified by the Thai Consulate.
5/ Get the MC certified by the Thai MFA.
6/ Get the KR22 from the Amphur.
7/ Include the KR22 as part of the marriage-based EOS application.
I am still trying to figure out the details, working with the following information sources:
Thai Consulate - I am on West Coast, and this region falls under the jurisdiction of the Thai Consulate in Los Angeles - https://thaiconsulatela.thaiembassy.org/en/index
The Certified Translations page at the Thai Consulate Website - https://thaiconsulatela.thaiembassy.org/en/publicservice/certified-translations?page=61b10e0827256e13033c1c62
The State Apostille - Select your state - https://www.nass.org/business-services/apostillesdocument-authentication-services
The DoS Office of Authentications page - https://travel.state.gov/content/travel/en/replace-certify-docs/authenticate-your-document/office-of-authentications.html