What is the best way for my fiancé to switch from a tourist visa to a Non-O retirement visa in Thailand?

Where was the location of the embassy in the United States?

Strange that you say the thai embassies in the US are behind on visa apps because it's all done online now with the eVisa website (by selecting one of the 4 consulates that issue visas for your state) and most people get approved in 5 to 10 days. 😕

If the person is over 50 and has the 800K baht in a thai bank account in their name only transferred in from abroad, they can show up on a tourist visa or visa exempt entry.

Once here they should go immediately to the main immigration office at the government complex (Building B) on Chaengwattana Road at Counter C-1 and get the hand out listing the requirements. <- I say that because they need a minimum of 15 days left on their entry stamp to apply so time is of the essence

Then get the documents together, go back and apply for the 90 day Non-O visa for 2000baht, wait the 2 week under review period and go back then to get the Non-O visa and a new 90 day stamp inked in

THEN wait until the funds are seasoned for 2 months in the account and there's 45 days or less left on the new 90 day stamp and go back to apply for the year extension for 1900baht

I don't understand the "they will be traveling on a tourist visa" part because to get a tourist visa for thailand you apply using the online eVisa website <- which is the same one you'd use to apply for the 90 day Non-O 😮

Anyway that's the process, and you only have ONE immigration office option in Bangkok for what you're doing; the main one out at the gov't complex on Chaengwattana Road.