I would take the same docs you had to use when you applied and got your non o with the bank statement letter ,that should cover everything , i heard you need to get the bank letter the same day you go to the office for your extension .The statement ,your tm30 proof of address and passport the 3 most important of course but take anything else you have in case.

Jesper i believe you can travel to Thailand with your documents of proof of earnings ect, go to the nearest embassy ( for me over the border in Lao )get your visa and extension if approved then to a bank as you said. I believe the difference is in your home country you will have to show health insurance to get the visa but in Thailand it is not required ,I am hoping thats correct as i plan to go to Thailand soon and do it all there with my thai gf .