The most straightforward approach is through a wildlife closure, so instead, head up the northerly fork along the riverbed for a few miles before crossing the hump to drop back down into the valley you want. From there it's a good slog up the moraine and glacier to your choice of objectives - the twin summits at the top of a headwall in the final cirque, or up an icefall on the right to a third peak. Crevasses and rockfall are constant hazards from the moment you step on the glacier.

If the crappy schist is not to your taste, there's a large wall on the east side of the glacier that looks like an outcropping of golden granite and has probably never been climbed. No idea how hard it might be...

Note: It is a little known fact that you can exceed the backcountry permit quotas in Denali with a climber's permit. These require you to be making a technical ascent and to camp on rock or ice, but you won't have to put off your planned climb because the unit is booked for backpackers.