Does your piggyback PPL have instrument privileges? It looks like they can put the 737 rating on your PPL and then transfer it to a stand alone certificate. If you don't have INST privileges the type would be limited to VFR ONLY which won't do you much good. You'd think if they will do that they would just add it to the stand alone certificate but they are the FAA and their ways are mysterious. You should check with the Airman Certification Branch in Oklahoma City.