I've done it twice, once during late August and the other time in early September, both times from Henrys Fork.
The weather both times was great, with a little rain during the August trip, and freezing temps at night for the September trip. Don't know about July weather. Both my trips were done humping in heavy trad loads, so as a UL trip it would be super fun. The only downside is all the horse poop, but once you get in a few miles there is less and less of it.
There are some little lakes and ponds just short of Gunsight Pass (about 10 miles in) with plenty places to camp, and with a UL pack you could make it from the trailhead to there in about 3.5 to 4 hours.
Looking at a topo map, it seems very tempting to take the "shortcut" across the huge boulder field beyond Gunsight Pass toward the summit ridge, which a friend and I did. It turned out to be a lot more work than simply staying on the trail, and there is huge exposure to ankle and leg injuries. I definitely wouldn't even think about it if going solo. The summit ridge requires quite a bit of rock hopping and some scrambling. On the August trip, there were afternoon thundershowers and there is the potential for lightning.
The most amazing experience there is the sky at night. If there is no moon the Milky Way stands out starkly, which is something those of us East of the Mississippi have rarely seen. Once your eyes adjust, you can actually walk around a bit by starlight. There is a new moon coming up July 8, so maybe it will work out for you.