As far as the skid steer goes, you had a track Hoe in the first group of pics. I take it the Hoe was not there to drag out the skid steer, bobcat, or what ever yall call it out of the buried hole. Also assume that you tried to use the bucket to push or pull while you drove it to try to get out.
I have used my F150KR to pull out a burried tractor out of a pond. Long story..... Tried to break the pond ice so that the cattle could drink. The Ice would not break until we drove out 15' on the pond and broke it with the Hay Fork. Then the tractor was stuck. Tried to back out in 4x4 and burried it more. I grabbed some drilling pipe and put a chain through the pipe and hooked it to the truck and the tractor. Using the pipe as a shock tube so that if the chain broke, my new tailgate or back glass would not be busted out. It worked great and the tractor came out real nice.
When you roll those tires off of the rims there are some interesting ways to reseat the bead.
1) Take a tow strap and wrap it around the tread and cynch it down and add air.
2) Take a flamable fluid and spray the inside of the rim and the outside of the tire and shoot a flame ball into the rim and when it blows up the explosion will reseat the bead and automatically blow out the fire. Then add more air to the tire.
3) You can take the tire off and take it to a truck stop and have them bead blast it. They will love how muddy it is.....
I personally like the flame thrower way along with a few beers or whiskey drinks