Non-slip differentials are available for the rear axles used by G3500 Chevy and E-350/E-450 chassis. 4x4 conversions are available for the E-series.
Traction will be less an issue than clearances on steep dirt roads, particularly exit angles and hanging up at center with long wheelbase models. C's typically have very long rear overhangs for load balanced to the axle capacities, and have clearance problems even on pavement. Mine likes to hang up going in and out of slightly sloped commercial driveways. But people do take these on dirt roads, where they know the road, and when they know their limits.
There have been C's specially built for the way you've used your truck and camper. Most are on conventional cab rather than van cutaway chassis, and many were made using 4x4 models and might be amenable to chassis lifts. In current production, look at C's from Tiger Adventure Vehicles. From about 10-15 years ago, there was an Xcursion line from Xplorer, a descendant of Frank Industries, one of the motorized RV pioneering companies. I think someone else has since gone into the business as Xplorer Motorhomes custom building a variety of models that will go where no conventional C motorhome can go.