Two-dimensional quantum dot (QD) arrays are considered as promising candidates for a wide range of applications that heavily rely on their transport properties. Existing QD films, however, are mainly made of either toxic or heavy-metal-based materials, limiting their applications and the commercialization of devices. In this theoretical study, we provide a detailed analysis of the transport properties of "green" colloidal QD films (In-based and Ga-based), identifying possible alternatives to their currently used toxic counterparts. We show how changing the composition, stoichiometry, and the distance between the QDs in the array affects the resulting carrier mobility for different operating temperatures. We find that InAs QD films exhibit high carrier mobilities, even higher compared to previously modeled CdSe (zb) QD films. We also provide the first insights into the transport properties of properly passivated InP and GaSb QD films and envisage how realistic systems could benefit from those properties. Ideally passivated InP QD films can exhibit mobilities an order of magnitude larger compared to what is presently achievable experimentally, which show the smallest variation with (i) increasing temperature when the QDs in the array are very close and (ii) an increasing interdot distance at low operating temperatures (70 K), among the materials considered here, making InP a potentially ideal replacement for PbS. Finally, we show that by engineering the QD stoichiometry, it is possible to enhance the film's transport properties, paving the way for the synthesis of higher performance devices.