I second Hesperus idea of the water with a nozzel to give it some velocity.
Also, I don't know how far the plug is up from the outlet, but if you could get a long rod or capped pipe and shove it up and try to ram a hole in the mess toward the top if possible or anywhere. Once you get even a small hole through, then water force from a trash pump would quickly erode out the remaining mud with the wood soon to follow. Or if you could do it from the top side. Just get a hole started and the water will do lots more having someplace to waste the wash out.
Those would be my suggestions. You have water near. All you need is a trash pump and a hose with a small opening to put it to use.
