Echo Park Road: truly would be horrible with significant rain. Sand Canyon would also be quite dangerous in flash flood conditions, as the road crosses the drainage more than a dozen times. One would be safe at the Echo Park Campground.
That said, the drive up and down is spectacular, and the EP area is wonderful. We had a lovely camp (no mosquitoes, although we heard they were bad earlier in the summer).
We did the hike to Mitten Park and back, taking a leisurely 4 hours to have lunch, search for rock art, etc. The rock art on the trail (about .3-.5mi from EP) is very good quality.
Some maps show a Mantle Cave, but we did not have good topos to this location and did not find it.
The road to EP goes right by Whispering Cave, highly recommended. One can squeeze a long way up to the right in the cave, which is delightfully cool.
At low water, one can wade out to the large sand island at the raft launch--refreshing.
Good tap water year round at the CG.