Been there twice, planning on a third trip next year. First two times we went in the beginning of April, early enough not many people go, late enough to usually avoid the snow. Next year we're planning on early-mid October for a rim-rim hike. I usually give them start dates in the week (vs weekend) and haven't been turned down yet. I do fax them in on the first day they accept them, just scan them into the computer and have it set up to automatically send in the permits so I don't have to be home for it.