Animal skeletal muscle exhibits very interesting behavior at near-stall forces (when the muscle is loaded so strongly that it can barely contract). Near this physical limit, the myosin II proteins may be unable to reach advantageous actin binding sites through simple attractive forces. It has been shown that the advantageous utilization of thermal agitation is a likely source for an increased force-production capacity and reach in myosin-V (a processing motor protein), and here we explore the dynamics of a molecular motor without hand-over-hand motion including Brownian motion to show how local elastic energy well boundaries may be overcome. We revisit a spatially two-dimensional mechanical model to illustrate how thermal agitation can be harvested for useful mechanical work in molecular machinery inspired by this biomechanical phenomenon without rate functions or empirically inspired spatial potential functions. Additionally, the model accommodates variable lattice spacing, and it paves the way for a full three-dimensional model of cross-bridge interactions where myosin II may be azimuthally misaligned with actin binding sites. With potential energy sources based entirely on realizable components, this model lends itself to the design of artificial, molecular-scale motors.