I'm in the prcess of excavating a stream (3" deep, 6' across, typically has about 6" water depth) where the water has been flowing for a few years, the bottom is a nice river rock and shale base. Solid. The sides though are a very organic and sand mix that if you hit with a spade, even during a drought, fills with water. Messy work. I've gotten my BX stuck twice so far. The first time, my neighbor came over with his Kubota and pulled me out. The second time, I had finally gotten a winch on a 2" receiver setup front and back and was out in minutes. Between the winch and having the BH stabilzers so I could lif the tractor and throw some logs underneath made all the difference. I am half way thrugh the project. Slow going because of where the material is going to end up and it is so moisture saturated, I cam only put down so much (4" layer at a time) or else I just make ruts and a mess. It takes a bit over a month for the material to dry out where it is being put down. This summer, I will probably be able to finish it.
What I learned was, if you cannot get unstuck in a few minutes, do not fight it. Accept the predicament and get the tools and help to get it resolved easily. Fighting it is a waste of time.