All I can find in the literature is that the cis→trans interconversion proceeds via dissociation of one of the PPh3 ligands resulting in a square-pyramidal Cs intermediate, with the remaining PPh3 in an axial position.
I assume it proceeds via either dissociation of the CO trans to the PPh3, followed by PPh3 and CO binding again to form the trans isomer; or via a Berry pseudorotation-like conversion of the square pyramidal intermediate, however considering that the former seems unlikely due to the CO being a more strongly binding ligand than PPh3 and the latter would require quite a bit of energy, neither of these make sense to me.