First off, I would say that there are North Yorks Moors experts on this forum who are probably more qualified than me to dish out routes, although I live quite close to thew NYM, I donl;t seem to get there to often.
BUT, it strikes me that as you're on public transport, you could easily do a linear walk rather than a circular one which I think makes the whole project a bit easier to plan (I'm completely with you on your reasons for doing this by the way, but anyway who needs an excuse....) 16(ish) miles is a reasonable distance too....
So, I think that the Northern scarp of the NYM - the bit overlooking Teeside is the best - its bumpier and has little crags for interest... and I think it would be a nice trek to follow the Cleveland Way Eastwards from Osmotherley - basically for as far as you can get, but see if you could get to the coast. If you cant get that far, you'll have increasing access to public transport to get you away, as you get nearer to Guisborough/the Teeside towns. Plenty of places for a discreet wild camp, and , as this is the "bumpiest" bit of the NYM, you'd get your exercise.....
