Unfortunately although the conviction is spent, the fact you went to prison is ALWAYS on the police computer and will always show in a PNC check until you are 100 years old.
They have already explained what you need. A Thai police record check. They are also not happy for some reason with your US back ground check.That's there requirement. That's the issue you need to deal with.
I wasn't entirely sure other than him saying between deliveries in Phuket. I was assuming boat delivery into Phuket but I stand corrected. Either way, continual visa exempt entry eventually comes to an end. Particularly for those from a certain age group.
They are mostly used for instance, if say a Nigerian who travelled from Nigeria to say the UK in order to join a ship. He wouldn't need a visa to enter the country where as he normally would. His seamans passport would carry a travel document and log of his travels plus a letter outlining exactly his travel plan. They are not that common and certainly not something just anybody could obtain.