New calendar year next january starts a new count. You will get a visa exemption. Have a ticket out and some usd on you. You will get 60 days. No problem.
If you were stateless and had stayed in thailand you would possibly be eligible. But you are not stateless and as a US Citizen none of that will help you in legal pathways. Your only option is to look at how a US citizen can become a Thai citizen. Those pathways are limited.
Just go with both passports and do the 30 day extension. You need a tm30 and a passport photo and an extension application. Doesnt take long. The immigration knows how to do it.