Bring a thick piece of plywood with you, maybe about 3 or 4 feet wide & throw that ontop of the mud & put your jack ontop of that. Should keep your jack from sinking. Just make sure your piece of plywood is thick enough to not crack (maybe 1/2 to 1 inch) and big enough to where it will cover enough ground to keep the board from leaning. If the junk yard will save you money, I say it's worth it. Good luck!