ZDC Controller reported that existing procedures make it very difficult to handle PIT arrivals transferred at high altitudes; alleging that a procedural fix would not be difficult.

Narrative

Air Carrier X was southbound on J53 at FL380. Air Carrier Y; FL390; was northeast bound on a vector to meet the SOP restriction for aircraft landing Pittsburgh. Off the vector; Air Carrier Y was descended to FL340 to miss two (point outs) aircraft from Indy Center at FL370 eastbound. Air Carrier Y had to be descended quickly not to only miss the two aircraft at FL370; but to try and make the SOP restrictions. Obviously separation is paramount and our job to ensure. That being said; the fact that there is no LOA with Washington Center and Atlanta Center for Pittsburgh landers is dangerous and unreasonable. As of now; Atlanta can hand off an aircraft at FL410; landing Pittsburgh; and we have about 40 miles to get the aircraft out of FL310 descending to FL290 to meet our restriction. This can be an issue with no other traffic; but throw in other traffic southwest bound; east bound; southeast bound from Washington; Indy and Atlanta it can create potential for error. There is an LOA with other Centers for aircraft landing just as far away as Pittsburgh if not further. It would be a simple and painless correction for everybody. Pittsburgh aircraft cross the Atlanta/Washington Center boundary at or below FL350 will be extremely helpful and safe.