I wouldn't necessarily vote for thaielite, but sticking PE visa at Chaengwattana is an option.
From an old instructions letter:
Staying in Thailand, you can affix Elite Visa at immigration Bureau Chaengwattana in Bangkok.
- Member who hold tourist visa, exempted visa or visa upon arrival have to book service 5 working days in advance for making the appointment with customer contact center.
- Member who hold non-immigrant visa, visa cancelation must done at immigration where visa was issued and do 7 days extension. Then, you could contact customer contact center for making the appointment to get Elite visa during this period.
- Member, who hold non-immigrant visa was issued from oversea, must leave country and could affix Elite Visa at Suvarnabhumi Airport. **Some nationality is required visa to enter Thailand**
Arriving in Thailand, member could affix Elite Visa at Suvanabhumi, Phuket and Chiang Mai International Airport. For connecting flight, we strongly require at least 4-5 hours gap between the next flights.