Well, you want to keep your rims so this might not be any help, but I bought rims with more offset so the tires stick out more. Keeps the frame rubbing down and widens the wheel base just a touch.

the rim width specs for the 33x9.5 is 6.5" to 8.5", but I think that the 6" rim would work. To find something to compare to, try to find someone who has/had something in the 235r85 series tires and see how those felt on the road. Those are kinda close in size, maybe not quite as tall. (245mm = 9.5")

Obviously it's not a sports car, so don't drive it like one and you should be fine on the street. And off road, don't air down too much and you should be fine with keeping the tire on the rim in side hill situations. Obviously you will sacrifice mud and sand flotation performance with a less wide tire, but I think trail and snow you will still be just great. And you are saving a little weight by going narrower too. I don't think it is a skinny tire, just not really wide like everyone uses to get through mud.

I don't think that the overall stance width difference of 1" (9.5 vs 10.5) is going to make much difference in stability. Maybe 1" wheel spacers to get a little wider track.

Bottom line, I think that if the tire didn't work or wasn't safe, BFG wouldn't make it in that size.