I've had to chain up my tires more than once to get out of a muddy area. My old Columbia would look at soft ground and get stuck before you even tried to move it. LOL Hurst
My truck would have pulled though that I think. Cross lock Diff lock Worst comes to worst I ask the dude in the dozer or jlg to give me a hand.
You can "rock" an automatic, but they aren't very happy about it. I've done it a few times, usually causes it to throw a code that has to be cleared later.