Maybe try dropping a line to the lovely folks at Toñito Hotel in Uyuni. They've been promoting tourism in the area for two decades and while they don't directly operate tours in the area they are connected with everyone in the community who does. Be sure to visit them and have a pizza when...
What Joe says. You'll have to skip some things like going over the Alto Plano via the 'fun' roads and I wouldn't take it out onto the Solar, but in general you'll have no problem, especially if you monitor the weather. Heck, I've seen mini vans driving Bolivia's "Death Road".