right now marrying in Thailand is better than marrying the United States. The fiance visa has longer total time than a marriage visa via another country marriage. Not to mention she will not be able to work or leave the USA during adjustment status. Either way you are looking at 1 year to 1.5+ total time.
The marriage visa however will give them a 2 year visa or 10 year with work permit depending on how long you guys have been married
this does not work lol. Even if you don't register it. Your Countries Embassy will have proof they gave you seals for intent to marry. All she needs to do then is take the translated Thai Marriage certificate to sue if she ever wanted to.