Have you driven on the "wrong side" much?
Andrew,
I know that the greatest temptation when setting up a roadtrip vacation is to pack as many places as seem possible into the route. Many people prefer this technique, and for that orientation, you would be better served to speak to travel agent -- Our focus is on the quality of the trip, not how many places can one drive through at warp speed.
A first concern -- is about road fatigue -- driving on the wrong side can be tiring and you will be driving a large vehicle on some challenging roads.
Go to Memphis and do the Elvis thing.
Looking at the route -- on Saturday after leaving NYC -- you mentioned Bethlehem (is this in Pennsylvania or is Blenheim, NJ?) I would guess from your intended visits, that you are a Civil War historian? One of the books you should consider would be "Along I-75" because of the depth of information about places to explore along that road. (http://www.roadtripamerica.com/read/Along75.htm)
From Memphis, I would suggest going north along the Mississippi River -- hanging a right at the Ohio and follow it into Louisville, (a fun place). We haven't been to the Mammoth Caves yet, but every national park is worth a visit.
Six days is ample to allow some R&R time for the return. Pittsburgh is one of our all-time favorite cities (especially at night) but be fore-warned it is built on seven large hills and can be tricky with RV's once you leave the major highways.
It should be quite an adventure.