I recently got married here, make sure you give yourself plenty of time if you do. I had to wait 6 weeks for an appointment with my embassy and the constant translation issues with the ministry of foreign affairs took another 2 weeks to sort out. Good luck.
I doubt Thai Airways will allow you to board, we had a massive row with them as they thought my wife's tourist visa to the UK wasn't genuine, best thing to do is go to the airport beforehand and ask.
My gf isn't Thai so probably best I get the landlord to do it with the link you provided. Am I right in thinking that the landlord gets a receipt and sends me a copy?