I found a link to an interactive map of state trust land.
Arizona State Land Department | Maps | Online Maps Click on 'start map server' in the Interactive Map section.
By zooming in to scale = .42 mile, I could see Cottonwood Canyon road (which is labeled as a road, so I assume it's a public road and OK to travel on without the STL permit), and following it I located Mineral Mountain Road, Woodpecker Trail, Ajax Trail, and Telegraph Canyon Road, which I followed all the way to Superior. A small section of Lower Ajax (trail) is on state trust land, as is the first few miles of Cottonwood Canyon Road. Woodpecker, Upper Ajax, and the area northeast of there is not STL. Also, Box Canyon Road is not STL. The Martinez Canyon loop is labeled as a 'road', and is also not on STL. I don't see any reason to purchase an STL permit unless I get excited about running Lower Ajax in my wife's truck some day, and the possibility exists that even that may be considered a 'road' as it's labeled on the map. I could go either way on that, but to know for sure I guess I'd need to talk to whoever enforces the law there. Problem is, they probably wouldn't truly know either- I suspect it would take a lawyer to interpret exactly where the public road ends. Camping off the first couple of miles of Cottonwood Canyon Road (TTORA) would surely require a permit, but you could just go down the road a bit and be out of STL. I'd have to say this is a non-issue, although I could see the authorities issuing a ticket (or hassling someone) in the belief that they 'know what they're doing', but it wouldn't stand up in court.
I looked for the coke ovens, somewhere near the 'Cochran Townsite', but couldn't find them specifically. However, the road to Cochran Townsite is labeled Cochran Road, and very little of it is on STL near the river. Cochran Road does meander through a few STL parcels farther south of the river, and there is a parcel in the vicinity a ways north of the river.
Here is the rule on crossong STL, from this page:
http://www.land.state.az.us/programs/natural/recreation_permit.htm
"ACCESS ACROSS STATE LAND FOR RECREATIONAL PURPOSES
Recreational access is outlined under State Land Department A.A.C. Rule R12-5-533(D). Under this rule a recreationist would need a permit to gain access to State Trust land or to other lands beyond Trust land unless traveling on a public road or highway."
I found a definition of a public road by the Arizona State Land Department,
http://www.land.state.az.us/programs/operations/applications/GroupRec.pdf
"4. “Public roads and highways” means the entire width between the boundary lines of every public road or highway maintained by the federal government, the State, the Department or a city, town or county if any part of the road or highway is generally open to the use of the public for purposes of vehicular travel."
To summarize all this crap, one of the trails (Lower Ajax) I looked for in the FJ area was on state trust land, the rest were not. Access to the trails across STL is permitted on public roads and highways, which are numerous in the area. I feel comfortable not purchasing a state trust land permit.
-Spike