This paper considers the challenge of tuning the gain parameters of an almost globally stable control law for use in a small spacecraft performing a large-angle rotation in low Earth orbit. Previous results have demonstrated the almost global stability of this control law by means of Lyapunov-type methods on the nonlinear space of rigid body rotations. With stability established, it is desirable to draw conclusions about the feasibility of optimizing this control law for specific applications. To this end, a genetic algorithm is used to search the space of admissable gain combinations for a specific controller design that yields optimal performance as defined by a user-generated fitness function. The controller design selected by the genetic algorithm is compared to that obtained using a trial-and-error approach. The genetic algorithm is able to rapidly search a large portion of the overall design space, and generally produces controller designs which outperform those found via trial-and-error tuning.