That's cool! I spent a lot of time hiking the canyon, mostly from the arched bridge to about five miles upstream of DCHS back in 09-10. One of my "things to find" was a mountain lion track. I found one track, near a little wet-weather tributary upstream of the arched bridge once. It was about the size you describe, but it wasn't real clear. I took some pictures, with my hand spread out above the track, but I can barely see the track. I'm not sure, but like Wizard said, it was too big to be a bobcat. I have to admit that I wanted it to be a mountain lion track, so there might have been some mental editing going on in my mind.
Most of the soil types around DCHS don't lend themselves to good clear tracks. The decomposed granite's too crumbly to make clear imprints unless it was "just right" wet when the track was made, and if it didn't rain on it afterward. The mud along the creek can be fickle, too...too wet, and it's just a hole, too dry and it doesn't print well.
Your 3-toed track is probably just missing the imprint of the 4th toe. There shouldn't be anything around there with just 3 toes, unless it had lost one. When you can find clear walking tracks, on flat surfaces (not climbing, scrambling, running, etc.) cat tracks differ from canines and bears by not showing claw imprints. Cats have retractable claws, so you normally won't see the claw imprints. Bears, dogs, coyotes, foxes, etc. don't retract their claws, so they normally make tracks with prominent claw marks. Also, cat tracks are generally a little wider than they are long, and canine tracks are generally a little longer than they are wide (not a lot of difference either way). The best way to identify or eliminate a track as being a bear track is that their forepaws and hindpaws make completely different-looking tracks. Both cats and canines look pretty similar front and rear.
Of course, the coolest way to identify the track is if the critter's still standing in it!