A man can do pretty much whatever he sets his mind to with enough determination and $$$.

Seems like your biggest obstacle is where to put the muck after it comes out of the pond.

For sure it can be dug out, but if you dig it out you need a place to dispose of it.

For sure it can be slurried and pumped out, but it has to go somewhere. A couple acre-feet of slurried muck pumped over the dam would make a god-awful mess if a monsoon rain came before the weeds grew up on it and washed a bunch of it down the holler. Could cause serious downstream damage and result in unhappy neighbors or DNR types knocking on your door.

Do you or a neighbor have pasture or crop ground? Might be able to pump the slurry into a honey wagon and use it for fertilizer?