I'm in NRD Philly closer to Baltimore, not pro-rec'd yet but I did my medical before my board at WRNNMC in Bethesda, MD. I realize that's a major hike for anyone in PA/NJ, but if MEPS is totally stacked up and you don't want to go to a contracted private doc, it might be worth the trip to DC just to get it done. You'll still need to work through your recruiter to get base access and an initial appointment, though.
I would also ask about the private doc option - you'll have to pay for it (around $120 IIRC), but my OR said Concentra was one of the approved providers. Google Maps says there are a few locations in the Philadelphia area.