We calculate near-threshold bound states and Feshbach resonance positions for atom--rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum
J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for
J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF
(J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.