  Recent experiments have demonstrated direct cooling and trapping of diatomic
and triatomic molecules in magneto-optical traps (MOTs). However, even the best
molecular MOTs to date still have density $10^{-5}$ times smaller than in
typical atomic MOTs. The main limiting factors are: (i) inefficiencies in
slowing molecules to velocities low enough to be captured by the MOT, (ii) low
MOT capture velocities, and (iii) limits on density within the MOT resulting
from sub-Doppler heating~[J. A. Devlin and M. R. Tarbutt, Phys. Rev. A
\textbf{90}, 063415 (2018)]. All of these are consequences of the need to drive
`Type-II' optical cycling transitions, where dark states appear in Zeeman
sublevels, in order to avoid rotational branching. We present simulations
demonstrating ways to mitigate each of these limitations. This should pave the
way towards loading molecules into conservative traps with sufficiently high
density and number to evaporatively cool them to quantum degeneracy.
