Once the shuttles start, you must use them from the visitors center up the canyon in the main park.
You must see the interesting formations going to the east.
I would not through the towel in yet! hook up your rig and measure it.
The overall height of the rig is the issuse in the tunnels. You must drive down the center of the roadway. It is a little disconcerning to stradle the yellow stripe.
I thing should advise is the length is not about the tunnel but more about the switch backs coming in or going out. East bound is easier as you are in most of the real sharp switch backs you are on the outside.
When I tow the big Suzuki I am right under fifty. I am different then pulling a conventional trailer. On the switch backs westbound many hitches drag as there is lots of marks.