I would like to share my experience as well. I have just returned to the U.S. after losing my AP while overseas.

I lost my advance parole while I was traveling in Asia. I went to the local U.S. embassy and they said that they could issue a Transportation (Boarding) letter to allow me return to the U.S. Processing time would be around a week because they needed to check with DHS in Bangkok, it would cost around $300 and I should present 3 Photos and a police report.

However, this country was not my last port before entering the U.S. (my return ticket was from Hong Kong). The consul suggested that I apply to the embassy in HK which I did. Given that there is a local DHS office in HK, I applied directly to it. After interviewing with an officer, he issued me two letters (one for the airline and another for the border officer at the US POE). I did not have to pay any charges. (My guess is that State charges the $165 while DHS does not).

I returned today from this trip and after a short wait at the secondary inspection in the airport I was admited to the U.S.