How To Move A Shed On Concrete Slab. A better option (although more expensive) is a combination of concrete piers and a lumber frame. A little more jiggling forward and back and the shed was sitting squarely on the concrete pad.
A rake and spirit level would be the best tool to help yourself in the leveling process! As a tip once you have the base plate and wall studs anchored to the concrete slab, put a bead of polyurethane caulk around the primeter between the base plate and concrete.
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As it only has to move 4 feet or so your proposal to cast a new concrete slab for it to move on to sounds a reasonable proposal. Before drilling the hole into the concrete ensure the shed is square.