I think half the problem stems from the "-egi"'s basically looking nothing like a summon we expect (ye ol "titan chicken nugget"), so what would Ramuh , Shiva, and Leviathan look like? Ramuh and Shiva end up looking like recolored Ifrit-egi's , and for lore reasons, logically we can not summon the actual primal. Players would probably re-glam them to carbuncle just so they occupy less space on the screen.
So maybe what is called for here is to make the primal-egi's at least be able to be glammed to the minion appearances. It's not like the game doesn't have those assets.
But maybe people like the existing ones. Another path to go is to take a page from "World of Final Fantasy" (Basically a game that you collect final fantasy monsters) and have alternate transfigurations of Ramuh (Ramewl), Shiva(Shivalry), and, Ifrit (Ifreeta), it's not like we didn't see an allusion to this in the first during the Eden's Gate raids. They made entirely alternate versions of each Primal.
There are plenty of other things Yoshi-P can let the summoner summon, and ways of customizing/glamor'ing them to suit the players taste.