US Immigration from Burkina Faso

My husband has his interview in 3 days, and if everything goes well we think he'll be able to to do the ceremony that afternoon, based on the experiences of others at our field office. He just learned today of *possible* work travel overseas in ~3.5 weeks. It is far from confirmed, and the date may change, so we don't want to put off his interview or ceremony. If, however, he does need to travel a few weeks after naturalization, am I correct that there are no options to get his passport quickly (beyond the 4-6 weeks "expedited" processing)? My reading is that USCs need to leave/enter using their US passport, so are you just stuck in the US until you receive your passport? It's not a life or death emergency, but it sounds like they could lose the contract if he can't travel when the client needs him to...