This paper investigates the tracking control of a multi-quadrotor slung-load system (MQSLS), incorporating a dynamic model that simultaneously accounts for underactuation, nonlinearity, dynamic coupling, and unmodeled dynamics. We introduce a novel force distribution algorithm, which bifurcates the cooperative control to two distinct components: slung-load position control; and cable configuration control along with quadrotor attitude control. Employing this strategy results in a cooperative controller that: (i) relaxes the constraints on cable configuration; and (ii) requires only up to the third time derivative of the reference trajectory. The proposed control scheme ensures almost asymptotic stability of the overall closed-loop error system under unknown constant disturbances affecting both quadrotors and payload. A comprehensive set of simulations and experimental results validates the effectiveness of the proposed control strategy.