The classical nearest-neighbor Kitaev-Heisenberg model on the triangular lattice is known to host Z2 spin vortices, forming a crystalline superstructure in the ground state. The Z2 vortices in this system can be understood as distortions of the local 120∘ Néel parent order of the Heisenberg-only Hamiltonian. Here, we explore possibilities of stabilizing further types of Z2 vortex phases in Kitaev-Heisenberg models, including those which rely on more complicated types of noncollinear parent orders such as tetrahedral states. We perform extensive scans through large classes of Kitaev-Heisenberg models on different lattices employing a two-step methodology which first involves a mean-field analysis followed by a stochastic iterative minimization approach. When allowing for longer-range Kitaev couplings, we identify several Z2 vortex phases such as a state based on the 120∘ Néel order on the triangular lattice which shows a coexistence of different Z2 vortex types. Furthermore, perturbing the tetrahedral order on the triangular lattice with a suitablecombination of first- and second-neighbor Kitaev interactions, we find that a kagomelike superstructure of Z2 vortices may be stabilized, where vortices feature a counter-rotating winding of spins on different sublattices. This last phase may also be extended to honeycomb lattices where it is related to cubic types of parent orders. In total, this analysis shows that Z2 vortex phases appear in much wider contexts than the 120∘ Néel-ordered systems previously studied.