  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. We suggest 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.
