Miltrade,
When you got stuck did you push the forks down to lift up your front tires and then try to back out? If you did not get any "lift" because you had the forks on the tractor instead of a bucket throwng some decent sized limbs/wood in the hole can give the forks something to push against to lift up the tractor.
But with those slicks on the tractor you still might not have been able to move backwards. Sometimes you have to go forward..
I have not gotten the tractor stuck to the point of needing a pull. The worse I have done was crossing two trenches with a load of wet sand. I happened to cross the first trench so that my rear tires where in the one trench just when my front tires went into the other trench.

I could push down with the FEL to get the front tires out so I had to dump the sand. That alowed me to lift out the front tires and back out. If I had been 6 feet in left or right of where I had the trenches I would not have had a problem. I just happened to cross the trenches where they were apart the same length as the tractor axles.
The most nervous I got was using the backhoe to cross trenches I had been digging. Long story short that hoe did not have enough length to get me as far across the trench as I liked. I was TOO close to the trench and in danger of flipping.

I would hate to have known my heart rate. I put retaining wall blocking in the trench so i could drive out. The trench was to lay the block so I had it handy.
Seems like you made rational decisions for each event its just when you added them all together they ended up being not so rational in hindsight.

Which is usually how it goes.
Why was the tranny in such a high gear? When I'm messing with stumps and such I'm in the low range and first gear. And often wishing I had a creeper gear.
Later,
Dan