Don't sweat Cottonwood Pass. It clears clears early even in big snow years. I've been over three times in big snow years in mid-June.
My guess is that the biggest problem along your route will be crossing Rock Creek. It's my understanding the log crossing is gone. This section of creek has big flows even late in the year.
As for New Army Pass, there is usually a cornice at the top, when snow is present. I've only been up in once when snow has been around. The cornice dropped between the climb up and our return from Langley. This was on a July 4th weekend after a mild winter.
