Yep, nothing I could do would get me out. As I think back, curling the bucket didn't seem to do much of anything. Moving the bucket stick left and right gave essentially zero movement of the tractor but did wallow out a bucket wide slit in the mud a few inches fore and aft. I could easily lift the front wheels out of the mud with the bucket lift, but that didn't help. They just spun in the air.
I should calculate the rearward force that the bucket curl can exert, given the cylinder sizes and hydraulic pressure, the offset distance, etc. Maybe someone has already done this. I bet it ends up pretty low compared to the force required to push 3 plates 6" wide by say 24" tall each horizontally through mud (the three sunk tires).
I'll try to take some photos of the holes left after the tractor came out. They're pretty huge.