I didn't mean to suggest Maximinus II was driving the consolidation, rather that the world was going in that direction and his types acknowledged and even supported the consolidation of pagan gods.
Are you considering Genius as a god? I see him as a personification of the people which explains why we don't have him honored by someone holding his head. The heads also come from Licinius. Note that Sol and Apollo shared a wardrobe designer at Antioch.
The Genius was seen to be present in many things. So on the POPVLI ROMANI issues, yes, it was the Genius of the People. When I see GENIO AVGVSTI on coins where he's carrying the bust of Sol or Serapis, I'm thinking the suggestion is that the divine spirit of the emperor is imbued with the attributes of those gods.