Previous Issues Addressed
Both issues (not strong enough and unwanted rack housing movement) were addressed with the redesign of the upper rack housing. The new design geared down the motor to increase the torque; it also modified the slots in which the racks were slid into.
The lift still wasn't strong enough. (In retrospection, I should've taught myself the physics acting in the system and base the design off calculations, as I did here). The other issue was the extrusion on the upper rack housing that supported the motor was too weak for the forces applied to it during lifting/lowering.