I oftentimes use the doubletrack loop (and sometimes some of the singletrack) at Manitou in Monticello for bikejoring and riding with my sled dog. I almost gurarantee you will not run into another rider. My dog has a tendency to sometimes get aggressive with other dogs, which is not a good thing with a 120lb Malamute, so I have to stick to the less trodden trails like yourself.
It's kind of overgrown right now, but the doubletrack loop isn't too bad, and you should be able to find your way around that. Check it out!
One other thing I'll add is that if you are simply concerned about your dog chasing things or running off, consider doing the bikejor thing. You can do it with any dog (some just need pedal assistance). All you really need is a harness for the dog, a line, and a belt. I get my stuff from this place, which is in New Germany MN:
For the line and belt, see ths page: http://www.blackicedogsledding.com/page10.html
Just get the standard hip belt for bikejoring. The deluxe seatbelt is nice for skijoring, but doesn't work as well for bikejoring.
I plan on checking out Salem sometime with the dog, but I'll be keeping her on the towline around there.