  Rigorous coupled-channel quantum scattering calculations on molecular
collisions in external fields are computationally demanding due to the need to
account for a large number of coupled channels and multiple total angular
momenta $J$ of the collision complex. We show that by restricting the number of
total angular momentum basis states to include only the states with helicities
$K\le K_\text{max}$ it is possible to obtain accurate elastic and inelastic
cross sections for He+CaH, Li+CaH and Li+SrOH collisions at a small fraction of
the computational cost of the full coupled-channel calculations (where $K$ is
the projection of the molecular rotational angular momentum on the atom-diatom
axis). The optimal size of the truncated helicity basis set depends on the
mechanism of the inelastic process and on the magnitude of the external
magnetic field. For dipolar-mediated spin relaxation in ultracold Li+CaH and
Li+SrOH collisions, we find that a minimal helicity basis set
($K_\text{max}=0$) gives quantitatively accurate results at ultralow collision
energies, leading to nearly 90-fold gain in computational efficiency. Larger
basis sets are required to accurately describe the resonance structure in
Li+CaH and Li+SrOH inelastic cross sections in the few partial wave-regime
($K_\text{max}=3$) as well as indirect spin relaxation in He+CaH collisions
($K_\text{max}=1$). Our calculations indicate that the resonance structure is
due to an interplay of the spin-rotation and Coriolis couplings between the
basis states of different $K$ and the couplings between the rotational states
of the same $K$ induced by the anisotropy of the interaction potential.
