My friend went to the Bangkok immigration office near Don Meuang (in Laksi Plaza/IT Square, 2nd floor, blue hall) while I was in Samitivej Chinatown about 2 months ago.
She took my passport, doctor’s letter about me not fit to fly, photo of me with the day’s newspaper, something in the photo with the hospital name and logo (a bag, in my case) and possibly a nurse, paid the B1900, and I got a 60-day extension of my visa-exempt status.
Everyone involved was compassionate and helpful.