Molecular orbital explanation of why the protonation of the oxygen atom makes a carbonyl group more electrophilic
Ignoring the presence of the positive formal charge on the oxygen


I think this is exactly what is responsible, even from the MO viewpoint. From the MO perspective, the electrophilicity of the carbonyl group can be viewed as how energetically-accessible is the $\ce {C=O \pi ^*}$ MO to the nucleophile's HOMO. The protonation of the oxygen atom effectively decreases the energies of all MOs of the carbonyl, including the $\ce {C=O \pi ^*}$ MO. Why? The proton is positively-charged. By attaching to the oxygen atom, there is a net decrease in the potential energy of the molecule due to there being more electron-nuclei attractive forces in the resultant entity. Hence, protonation makes the $\pi ^*$ LUMO more accessible to the attacking nucleophile, increasing electrophilicity.