I was trying to leave a nebulous (lazy) comment ><
Honestly, its a story and stories can change through twist and turns that don't kill cannon. If you wanted to summon a summon that was a visual imagine of the creatures we have grown to know all so well through the years I don't think it would be that hard. It could be something similar in the vein of 11.
It would take a lot of writing, but you could do quest(s) that lead you to the point of being able to summon a piece of whatever summoned you've earned (through aforementioned quest). Like 11 (using 11 for brevity rather than wanting a clone of that system) you could summon an actual shiva, but in storyline wise its just a fraction of her power she has bestowed upon you. They (the summons) give the smallest of their ethereal essence to people deserving of their power to wield as they see fit.
If they're Gods then it makes sense for them (through the idea of summoner in the first place through general FF lore) to have Avatars or disciples of their power running around. A little writing can add a whole bunch of things.