Fatty acid mega-synthases (FAS) are large complexes that integrate into a common protein scaffold all the enzymes required for the elongation of aliphatic chains. In fungi, FAS features two independent dome-shaped structures, each 3-fold symmetric, that serve as reaction chambers. Inside each chamber, three acyl-carrier proteins (ACP) are found double-tethered to the FAS scaffold by unstructured linkers; these are believed to shuttle the substrate among catalytic sites by a mechanism that is yet unknown. We present a computer-simulation study of the mechanism of ACP substrate-shuttling within the FAS reaction chamber, and a systematic assessment of the influence of several structural and energetic factors thereon. Contrary to earlier proposals, the ACP dynamics appear not to be hindered by the length or elasticity of the native linkers, nor to be confined in well-defined trajectories. Instead, each ACP domain may reach all catalytic sites within the reaction chamber, in a manner that is essentially stochastic. Nevertheless, the mechanism of ACP shuttling is clearly modulated by volume-exclusion effects due to molecular crowding and by electrostatic steering toward the chamber walls. Indeed, the probability of ACP encounters with equivalent catalytic sites was found to be asymmetric. We show how this intriguing asymmetry is an entropic phenomenon that arises from the steric hindrance posed by the ACP linkers when extended across the chamber. Altogether, these features provide a physically realistic rationale for the emergence of substrate-shuttling compartmentalization and for the apparent functional advantage of the spatial distribution of the catalytic centers.