A coarse-grained model for surfactant molecules adsorbed at a water surface is studied at zero temperature to elucidate ground-state tilt ordering. The surfactants are modeled as rigid rods composed of head and tail segments, where the tails consist of effective monomers representing methylene CH2 groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In this work, we study the effects due to variations in both the head diameter and bond length on transitions from untilted to tilted structures and from nearest-neighbor (NN) to next-nearest-neighbor (NNN) tilting. Coupling between tilt ordering and lattice distortion is also considered. We provide a molecular derivation of a scaling relation between tilt angles and distortion obtained previously by phenomenological arguments. Due to the discrete site-site nature of the model interactions, the predicted ground-state phase behavior is much richer than evidenced by models employing cylindrical rods. In particular, we have found transitions between different phases (i.e., NN-NN' and NNN-NNN') of similar symmetry, which may have experimental support. We have also examined the sensitivity of the transitions to details of the model, such as replacing Lennard-Jones head-head and head-tail potentials by purely repulsive interactions.