We compare the time- and angle-dependent strong-field ionization yields of three molecules with very similar electronic structure. A pump pulse in the deep ultraviolet excites 1,3-cyclohexadiene, α-terpinene, and α-phellandrene to their first excited state. The latter two molecules are alkyl-substituted 1,3-cyclohexadiene systems. We then measure the strong-field ionization yield due to a near infrared probe pulse as a function of delay and angle between pump and probe polarization vectors. Ab initio electronic structure calculations allow us to associate the parent ion yields with removal of an electron from a LUMO orbital (occupied after excitation by the pump). Despite the fact that the LUMO orbitals for these molecules are very similar, the angle-dependent yields are very different, indicating that it is not the orbital shape alone which determines angle-dependent ionization yields.