OK, that makes so much more sense! You'll have a great time then. THe opposite weather warning applies - the top of the La Sal loop can get snow, so you'll need to pick the right day for that.
I've seen that path - didn't know what it was called and forgot about it, jumped to a wrong conclusion about which path you meant. It's just on the west side of the highway, and looks like a great way to get away from the cars. Does it go all the way into Canyonlands, or just get you to the start of that road? Either way, looks like a good one.
Sounds like a fantastic trip!
Other camping options are a couple of forest service campgrounds on the river road west of town and staying at the Lazy Lizard hostel (if you want indoors).