I would go from 13-23rd. I wouldn't be too concerned about muzzleloader season. I just feel like the first week of the season can be really hit or miss depending on how hot it is. I have always had my best luck right in the middle of the month. Thats also usually when I see the most rut activity.
Last week of the season, north facing slopes with cover, food, & water source, as far away from any motorized vehicle road/trail, in terrain only a fool would want to go. Hike in 6-7 miles, setup camp, then start putting the miles in everyday.....
Northern New Mexico seems to be just getting "good" as the archery hunt ends, around Sept. 25 or so. I am considering archery hunting the muzzleloader season there, but the season is shorter.