I have, and still hunt a lot of public land. That draw of yours should be awesome. I happened to ride thru that area this past summer and really looked enticing to me.
As to hunting land you've not seen., Best bet to increase odds if boots on the ground is limited, is find areas with intersecting Edges. By that i mean it can be anything from conifer to hardwood, field to forest, types of hardwood against another mixture, topography variations creating edges,etc. Deer are lovers of edge, and I have more than once went in at barely daylight and picked a spot with a mixture of those mentioned and scored. The more intersections of various type of edges coming together in one place and taking the wind currents into consideration, and you will be very amazed at your success on such a limited access ground. I wish you the best of luck and there is no greater feeling than succeeding under such conditions. And remember, your success may not necessarily the taking of a deer, but the joy of the effort itself. Taking game is just the bonus. Good luck, I am envious.