I just received my new passport in Bangkok yesterday.
Total processing time seemed pretty quick.
May 7th, mailed passport to embassy.
May 8th, passport received by security at embassy.
May 23rd, got State Dept email that it is being processed.
May 24th(!), got email that the State Dept had sent it.
June 5th, it arrived at my home via the prepaid Thai Post courier envelope.
Aside from friendly replies to my questions via the contact page, I never received any confirmation from the embassy itself that they had received my passport or mailed it.
Also, the Thai Post tracking system never could find my courier tracking number, even though they had obviously recently mailed it to me...
Overall, it was painless and fast, but it was pretty stressful not having any idea where my passport was for about a month.