We went to the Bangkok IO to extend our STV, and found out there is, in fact, a list of required documents that does not seem to be available online. I have attached it here.
Note that the 4th bullet on the right says "Proof of Thai health and accident insurance..." When we got our STV we opted not to go with the suggested Thai insurance companies since their premiums were quite high for the minimal coverage. We used another carrier who was already setup to provide the special Thai insurance certificate with 3 signatures (they had even automated it, so it was produced automatically with the rest of all the official paperwork). The Embassy in the US that issued the visa was happy to accept it.
However, the officer at the IO said we had to have insurance from a company in Thailand. We politely pushed back and said surely this was a mistake - we bought a $1M USD policy with exceptionally good coverage (and we spent less than we would have paid a Thai company for far worse insurance). I suspect the officer was misunderstanding the use of "Proof of Thai ... insurance" to mean that it must be from a Thai company, but, alas, there's nothing we could do.
Has anyone else had this experience?
Also, near the bottom there's a bit that's cut off that seems to say the last day to extend an STV is September 30th. I've read this elsewhere and believe it's likely true. Just FYI for anyone this affects.