Since nobody else has replied, I'll give you my input, even though I haven't been through the canyon in the fall. I'm going to guess that you're not going to get any beams that late in the year. The canyon is narrow and deep, so you need the sun to be overhead in order for any direct sunlight to reach the canyon floor. I would guess that by August, your potential for beams is greatly diminished.
I would still visit the canyon, though. The colors of the canyon walls earlier and later in the day are just stunning, and I've made some of my favorite images when the light was low.