Note that doesn't come into effect until the 26th of January. Also, if you're unable to find a testing location, SOME embassies will issue a waiver depending on the country. Not sure what the US embassy in Bangkok will do.
Which embassy did you apply to? I have not heard of anyone in the US being granted an STV. I emailed the embassy in DC a couple weeks ago asking about the STV and they never responded either.
Start with your closest Thai embassies website. There is an online application for the Visa, fill it out and submit it. When requested, mail your passport and supporting documents. After you get your passport back, then you can apply for a COE. All the instructions are in the email they send you.
Do you meet the legal requirements for you position? If so then you don't need an agency to facilitate the visa change. A letter from your employer and a couple documents from them showing they can employ forigners is about it.