Other axion searches on the table includes GALILEO.
https://phys.org/news/2024-03-galileo-scientists-method-dark.html
It may work, however they are not very compelling IMHO.
Cosmologically they are a bad fit to cold (heavy) dark matter. Quantum physically they have a gravitational coupling problem I believe (most of the potential mass range has too short lifetime to exist as primordial dark matter today). Finally standard particle CP symmetry breaking is better explained by its finetuning (CP symmetry; finetuning factor now in the minimum range of 1,000 - 1,000,000 without any axions involved) and neutrinos (mass oscillation CP breaking the putative axion symmetry now at 2 sigma significance).
I believe you mean massless matter since other mass energy is explained (mostly by dark energy) and there isn't any "matter distanced mass". But radiation is an insignificant part of the universe energy budget after the first 10,000 years of radiation dominance (albeit primordial photons of the cosmic background still outnumber other particles with a factor 10^10).