1) Wright offers two meanings, but the one which best fits the examples noted here is that it was a kind of fork, one with the tines set at an angle which made it easier to drag muck out of the midden.
1535 three mukforkes ijs ... foure pitche forkes xvjd ... iij mukdragges xijd, Stillingfleet
1578 One mucke dragg, two iron forkes, Ripley
1581 2 pyckforkes, 3 muckforkes and one muckdrack [sic], Anston
1610 Item two Muck Forkes, one Muckdragge, Kirkstall
1748 one muck drag, Sowerby. A rare York by-name may have been occupational, for the labourer whose job it was to move muck with such an implement: 1340 Alanus de Wifestow, mukdragher.