Having Halo on your mind, it is unlikely someone will look back into cycles of curves with pairing. It is just hard (citing “arguments against knowledge” paper from the MNT5 inventor):
Still we might look into hyperelliptic curves with pairing. The idea is, number of group elements (pairs of curve points) scales roughly quadratic of base field cardinality, in case of quintic polynomial. There should be plenty of searchspace for a subgroup of the proper prime order, hopefully completing a cycle with a BLS12 curve.
Pairing on hyperelliptic curves was discussed with Dr.Nelasa around 2018.