No need for the Chiang Mai letter unless asked. Highlight the deposits from clients in your bank statement for ease of understanding. A very brief cover letter explaining your work, that you won't have any Thai clients, and any other tidbits you feel relevant.
Enter Thailand visa exempt, go to a dentist, enquire and explain you need a diagnosis and treatment plan document with scheduled appointments. Go to a neighboring country and apply, wait for approval and return to Thailand.