Free: Contests & Raffles.
638 will fit your requirements except you'll probably only be 2-3 miles in. But you will definitely be in back country. And you won't find any tougher terrain to hunt elk in.
I won't narrow it down to a specific unit but if it were me I'd be looking at the Gifford Pinchot National Forest.
Get deep into the Packwood GMU 516. Or, head south to trout lake.