Are you certain you cannot get a certificate of residence from the US consulate or embassy? I've gotten them numerous times from the consulate in Chiang Mai on visa exempt.
I hope you're right about that. I know of two friends here in the US who were denied visas (METV) and both lost their $200 application fee. Thankfully I haven't after three applications.
I just completed a 5 month visit to Thailand. I showed evidence of my both my arrival flight and my final departure flight. I took care of the two required exits while there.
Perhaps consider the METV (Multiple Entry Tourist Visa). It's perfect for stays for up to 180 days with unlimited exit/reentry and no interactions with immigration. You are required to exit prior to each 60 day stay to extend the visa for it's duration. I don't know your status but as an American you might find it prudent to consider being in the US for part of the year to use your Medicare coverage. You'll also find it easier and less costly to purchase travel insurance to cover you for the time you're in Thailand.