no extension requires a background check. There's one retirement visa that requires, which is the OA visa. But it has many other requirements and is not the visa most people want for retirement. The non-O is what most people want and the only real requirements are being over 50 and showing the correct amount of money.
You would be able to use income to get the 90 day visa from the Thai embassy, but you wouldn't be able to use it to apply for an extension from immigration once you're in Thailand. The ONLY thing you can use for the first 1-year extension in Thailand is 800,000 baht in your Thai bank account or embassy certified income, and the US embassy does not offer that.
if you apply from a Thai embassy you can get the 90-day visa which will let you open a bank account once you arrive in Thailand. And that will let you prepare to apply for the 1-year extension.