Your problem is going to be the FAA does not grant many DPEs 737 authorization. I was looking a few years ago and there was one. The FAA wants pilots getting a type rating in a transport jet to go through a 142 school. The 142 school will have what you would think of as DPEs who are called TREs. But their authorization is only good for students who have gone through the 142 school's program.
You say you have a FAA commercial with a 737 rating. Is it a full type rating or just the make ICAO happy SIC rating? If it is a regular type rating and you pass an ATP checkride in a little twin, the 737 rating will move up to the ATP level. The idea is you were held to ATP standards for the type ride even if you did not have an ATP or didn't have the time to make the type ride an ATP checkride. So there is no reason to repeat the ride.