If you use a snatch block, and double the cable back to your car, then you'll effectively double the capacity of the winch, reducing the strain on it.
The single line pull capacity will be 3500lb, and a double line will be close to 7000lb.
I think this would work just fine for you, unless your 31" tires are completely stuck in the mud, then you may not get unstuck with the winch alone.