Kathmandu to Tibet then transit Chengdu to Bangkok

I have a US passport and will be traveling with a group from Kathmandu to Tibet and the tour company will be obtaining the Tibet travel permit. However, the tour ends in Lhasa and then we are responsible for flights out of Lhasa to elsewhere. The day the tour ends there are no flights Lhasa-Kathmandu. I want to fly to Bangkok but it looks like the only option is to connect in a Chinese city (most likely Chengdu). It is a 3 hour connection, I would not be leaving the airport, would directly connect to the flight to Bangkok. I don't think I would qualify for the visa free transit program because I am coming from Tibet, and it sounds like I would have to return to Kathmandu to get a China visa which I can't do because of flight schedules. Is Lhasa-transit Chengdu-Bangkok going to be possible?

Thanks - Karen