Well, its been a few years since I've been out there- went to college in Flag- but your long-twisty-road description describes almost all the cool places in northern AZ. *chuckle*
Most of the jeep trails that I know of are along the rim of the canyon and then you hike in. There's a great creek that runs along the bottom and a trail trail sorta follows it. But, between the topography of the area and the nature of wildland fires, there's no way a fire team will go into that canyon. I don't know if it's actually burning, the posted article suggested that it might be in danger. Portions of it have burned before.
Here's a topozone link of the area. Lots of "Sycamore Canyons" in AZ, but this is the wilderness area ESE of Williams.