Aren’t many winches out there that’s gonna help a backhoe get unstuck.
Best thing you can do is get more stone where you are working.
What you can do is, practice.
Get the machine up in the air and figure out how to move using the hoe.
You have to move it side to side, lifting the back of the machine off the stabilizers and sliding it to the sides and even forward and backward.
You can use the loader bucket also, figure out how to tilt the bucket back a little so it won’t dig in when pulling or pushing the machine with the hoe.
You will be amazed how much you can move the machine, with just the hoe.
Practice putting it in gear, in low with the tires off the ground, lift the machine, slowly lift the stabilizers, so when you put it down, it will drive itself as you lower it with the hoe.
When I lived in Tennessee, the clay, when wet, would stick any wheeled machine, even with 4x4.
I ended up bolting a used rim that I made, that I bolted to one of the rear wheels that stuck out as far as the stabilizer. That made it a drum and I cut a hole in the middle for a chain hook.
When I got stuck, I would run a chain to a tree and wrap it around that rim, as the rear wheels spun, it created its own winch, with the chain.