I have been reading this recent paper of J.McKay and YH. He (they've written a number of papers recently, including a fun and joking one on 42 which overflow commented on) called "Sporadic and Exceptional"
There are some old ideas which are summarized and some new observations and numerology. Whatever it is, it seems like some kind of over-arching set of correspondences linking Monster/Baby/Fischer versus E8/E7/E6, i.e., the largest sporadic groups versus the largest simple exceptional Lie algebras, using cusp numbers and enumerative problems on del Pezzo surfaces.
However, numerology aside. Anyone have any ideas/comments on how to find the geometric significance of the cusps and why they are relevant to Moonshine and to this current context?