Un -hook that field cultivator pull the tractor out with another tractor. Then pull the cultivator out from the back with a chain. Been their done that. More than once.
I'd get a 200 size (45,000 lb.) or so size excavator to dig out the wheels and dig a "ramp" up to firmer ground. That's a big machine to bury up to the tops of the wheels and then try to pull out.
this pic. has been all over the net. in fact I think it showed up last spring when it was wet here in the midwest. I would dig away from it with a 44,000 pound hoe and then hook a good sized cable and pull it out. If you are the owner or operator of this machine you are a fool for taking the x-tra time to stick it even worse. Been there done that and leaned my lesson........