Bruce,
There have been some good suggestions already. I would like to build some trails similar to what you are describing. In my case the trails would be for mountain biking but the concepts are exactly the same. I attended a weekend course sponsored by the International Mountain Bicycling Association (IMBA) about how to build sustainable trails. My advice would be to take it slow and do your homework before you hire anyone.
The type of trail you want to build has some very specialized requirements that most dozer and excavator operators don't understand. If you don't build this trail correctly, water and vehicle wear will destroy the trail in an amazingly short amount of time. I have a neighbor who had a dozer operator build an ATV trail down a steep slope. The trail ended up so treacherous that my neighbor won't drive his ATV down it. The dozer operator was not incompetent; he just didn't have experience at building ATV trails on a steep wooded hillside.
A good online guide for trail construction can be found
here.
Also, here is an outstanding resource that would well be worth your time to look at before starting this project. I have this book; it was put out by the
IMBA.
The IMBA has some online tips for trailbuilding located
here. Look at the related links at the right side of the page under
Trail Building and Design. One particularly useful page is called
Designing and Building Sustainable Trails that you will want to check out. A good concise trail construction guide with drawings is located
here.
There is some conflicting advice in this thread regarding how to slope the trail. IMBA says you should use "Outslope" meaning that the trail will be sloped so that water runs off the trail down the hill, not down the trail or toward the "bench" cut into the hill. I have a road that was cut so that it was "Insloped". That road is now unusable because water has eroded 3 foot deep trenches running down the road.
Also, building switchbacks is a very technical skill. Most dozer and excavator operators don't know how to build one. If you don't do it well, you will end up with a turn that will either erode to the point of being unusable or will be hazardous/dangerous to drive an ATV around. The safest, most sustainable (i.e. doesn't erode) switchback design is called a
Rolling Crown Swithback. Since your grade is more than 7%, you don't want your turns to be "Climbing Turns". You will want Rolling Crown Swithcbacks. However, if you talk to most excavators about these turns, they will have no idea what you're talking about and you'll end up with climbing turns that may be very difficult for an ATV to traverse.
Lastly, trailbuilders use specialized equipment that works on steep slopes for narrow trails. Some examples can be seen
here. You would be best off hiring someone who specializes in building trails, not roads. You can start looking for contractors
here.
Good luck with your project. When you start, please post pictures!
Obed