My wife and kid just got on board from Japan to Thailand. She made a mistake not getting the letter from embassy but it's application form. We emailed from airport to the consulate with photos of the passports, doctor certificates, tickets and the application form that has such information as ID number, Thai address, etc. Then called the consulate, saying that the flight departs in 2 hours. Despite being before its opening hours, the consulate prepared the letters and emailed back to us in 10 minutes! Bless these guys!