Wyoming Mule Deer Lottery Success-Need Advice

[DocHunter]

I have been drawn for a Wyoming Mule Deer Lottery tag and have been informed that the hunts begin September 15, 22, and 29. I will be hunting about 60 miles south of Jackson Hole. Outfitting will be provided by Great Plains Outfitters. Can anyone give me any advice regarding which dates to choose? I spoke briefly with the outfitter who said he could not really suggest one over the other, except that the first would be more crowded. Apparently residents can get tags over the counter and hunt the area we will be hunting. I am inclined to go to either of the other two dates, but would welcome any suggestions. I will probably be using a Remington 700 BDL in .270 with a Ruger No. 1 in 7x57 as a backup with handloads for both.
Thanks.