We perform a theoretical study of the effects of electronic correlations on the superconducting gap structure of multiband superconductors. In particular, by comparing standard RPA-based spin-fluctuation mediated gap structures to those obtained within the FLEX formalism for an iron-based superconductor, we obtain directly the feedback effects from electron-electron interactions on the momentum-space gap structure. We show how self-energy effects can lead to an orbital inversion of the orbital-resolved spin susceptibility, and thereby invert the hierarchy of the most important orbitals channels for superconducting pairing. This effect has important consequences for the detailed gap variations on the Fermi surface. We expect such self-energy feedback on the pairing gap to be generally relevant for superconductivity in strongly correlated multiorbital systems.