I just got back from LAC two weeks ago, and you're not going to need any more than one camera. My g/f used a 5D, and I used a Panasonic LX5 on a tripod, and it's FAR narrower than UAC and more trouble getting around in, esp. w/the ladders (especially the last one before exiting).
She altered between her wide angle and a 70-200 TP, and it was a pain in the butt for her, esp given the amount of ambient dirt and dust.
There are, however, far less people, and the photographers pass should get you more time than you'll ever need.
Whatever you do, however, LOOK UP. There are all kinds of odd angles and interesting effects the light makes on stone right above your hear. Lastly, both she and I use detachable viewfinders, mine electronic, hers a Canon right angle job. Highly recommended. That, and we were there at what's usually thought of as a crappy time of day (after 1100 in the morning) and while not ideal, there was plenty to look at/shoot.
This was looking straight up. I just wish I'd taken a shot of the entrance. When you first see it, you'll wonder how it's going to lead into what it eventually does.