OMG, I can totally see something like this for Smn, not so much the transformation deal because it would steal Reapers thunder, but the whole Jojo stand thing for sure could be something for Smn.

-Get rid of Ifrit, Garuda, and Titan as separate pet entities and instead change "Summon" into more of a stance/stand, rather than having pet out and following you.

-Summon can grant an aura around the Smn relative to the summon, fire for Ifrit, wind for Garuda, earth for Titan, or if they can get some pro effects working, the egi can just hover right behind or around Smn shoulders kind of deal.

-Keep the Egi Assault but then when Smn uses those, there is not longer a delay for the "pet" to act because the Egi will now be more of a spell effect rather than a separate entity.
Example: Using Burning Strike with Ifrit could then have Ifrit phase in next to the targeted enemy with a fiery effect, slash the target then phase out or return to the Smn.
Example: Using Wind Blade with Garuda could have Garuda pop in and hover over or side of the Smn, and shoot out a Wind Blade then phase away or return to Smn.

So yeah doing something would fix the pet delay response cause they would basically just be very fancy skill effect rather than full on pets.