I hunted the Genessee area throughout the 4 years I attended the Univ. of Idaho; you are already a step ahead of the rest by having permission on private ground. I'm curious to hear who's ground you are hunting on, a good friend of mine farms a couple thousand acres in that general area. To get back to your question there is some good whitey's there, the 10 days you are hunting would be the exact same 10 days I would have picked given the opportunity. You will see it all, pre-rut and possibly mid-rut, depending on when it hits this year. Spending time around there I would hold off on a good 4x4 (125"+) or a good 5x5 (140"+), but again that is my opinion. I have seen some good whitey's taken off of private ground, one in particual hit the 165" in 2002 from a friend of mine.
It's a good area, you will have fun no matter what the outcome is. Bring the shotgun, the pheasant hunting isn't half bad either. Good luck!