My knowledge of the North York moors, is that they have the steepest gradients on the West side (Northallerton) most of which I would not tackle myself at present, untill I get a compact and loose a bit more weight, The South side (York) is more manageable with longer shallow climbs. Near Whitby, Egton Bridge area I found 30% gradients which I have to walk. I know very little of the North side so cannot comment on it apart from the Esk Valley which has some steep climbs both side of it.
As for traversing the moors, most roads run North to South across them, and from the West to the East there is no road that I can see you can take direct from one side to the other unless you dog leg constantly North to South from one side to the other.
Bear in mind also, at this time of the year it could get cold on top of the hills so be prepared for it.
My last foray over them through the middle, 60 miles left me worn out when I got to Whitby, as it is quiet hard going, and I still had to return back over them. 120 miles in nine hours
Oddly enough I was looking at the map myself today for another ride out onto the moors before the days get shorter. Apart from that it is a great place to cycle over.
