Lower air pressure will help a soft surface support the load in sand, snow, or mud. I don't know how much it helps with traction, but it will sure provide better control and help you not get stuck. This is an unusual requirement, where you're looking for traction in non-drive wheels. Once they lock up, you're plowing furrows. Chains might help, but they might also just tear into the rocks and road surface and beat the wheel wells up.
We have so much trouble enough finding good trailer tires that I bet the tire manufacturers haven't even thought about your requirement, let alone build a tire for it. My first thought is to look for a light truck tire with good tread in the right load range. What you really need, of course, would be something more like a tractor tire, but on a TM scale. How about the tires they put on Bobcats? My dad used to own a Bobcat that had 3 Bobcat tires and a light truck tire, all mounted on Bobcat wheels, so there's a precedent for you. Tractor or Bobcat tires won't be made for highway speeds, of course, so you'd have to swap them on when you get to the dirt. But it might be good enough to work as a spare in a pinch, if you were willing to drive awhile at slow speeds, so that you could carry one less tire.
This came up in Google:
http://cgi.ebay.com/ws/eBayISAPI.dll...m=270572242695
Looking forward to the next installment in your story!