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The correct approach to moving the vertical center of a Rack and Pinion hoist involves adjusting the tie downs and wall ties. These components are crucial for properly aligning the hoist with the structure it is mounted on. By adjusting the tie downs and wall ties, you can create the necessary adjustments to the hoist's position in relation to its vertical line of travel without compromising the safety and stability provided by the hoist's design.

Adjusting tie downs and wall ties allows for proper alignment and support, which is essential for the effective operation of the hoist. If these adjustments are not made correctly, it could lead to misalignment, causing operational inefficiencies or safety risks during use. The other options do not directly address the need for moving the vertical center in a safe and effective manner. Therefore, adjusting tie downs and wall ties is the appropriate solution to the request made by the contractor.