I'm in Harrisburg, PA with a good bit of knowledge of what's here in central PA. Michaux State Forest is located in the southern portion of the Pennsylvania and offers some dirt roads from route 34, west and south into Maryland. A lot of our mountain ranges seem to run east/west, and as such a lot of the roads through our forests also run that direction.
Tuscarora State Forest offers some dirt roads with the help of several miles of pavement to go from Newville, PA area north towards Lewistown, PA. Then you have Rothrock and Bald Eagle State Forest. Bald Eagle State Forest will probably get you further north and east. Then maybe transfer into Tiadaghton State Forest, Sprout State Forest, and Susquahannock State Forest. I've never been in any of these, but they make up a majority of north central Pennsylvania.
I'd estimate traveling through Michaux, then getting into Tuscarora to Lewistown area would be a full day. Really not sure about the northern reaches.
Let me know if I can be of any help for the Pennsylvania section.