Thank you, Keith!
I was there in early November of 2015, and took this image at 12:55 PM, according to the EXIF and my memory. Early afternoon is the only option if you go there in the fall, because you don't get much of the daylight to start with, and also the hike in and out takes about 4-5 hours each way.
We started as early as we could, possibly around 7 AM, and stopped only a few times to shoot the Archangel waterfall, which is very close to the Subway. We were at the Subway just past noon, and another problem is that the place is pretty narrow and small, so you have to take turns with other photographers. All in all, you only get about 30 minutes to shoot there, because there is always a line of other photographers waiting to get in the canyon. That and the hike itself would be the only drawbacks, but I would still go with any opportunity; the place is so worth it. Even without a camera, when you are standing there, it is an amazing feeling to see all those colorful walls, big pools, and rock formations. I would highly recommend visiting and photographing the place, just make sure you prepare well for the trip. Good luck and have fun if you go.