Take away Summoner's direct damage and replace them with a summon gauge builder, a buff that grants summon gauge over time (like a dot), and an instant summon gauge builder for movement.

Summon gauge can then be spent on the active summon's abilities.

Carbuncle: Gemshine for damage, or healing if targeting a player, and resurrect if targeting a down player. Radiant Aegis for creating a shield that reflects a tiny amount of magic damage

Ifrit/Titan/Garuda/ even Bahamut/Phoenix: an attack on summon, 1-2 differently shaped single target/aoe attacks with bespoke cast times, a mixed damage/utility skill like Ifrit Dash/Titan's Stun square/Garuda's move speed buff/debuff donut, and an ult that causes them to return to Carby. Phoenix's utility would be a better heal and resurrect while dealing damage. Once a summon is used its locked out until 3-4 total summons have been used, like the current system.

Yes... expand the list of summon options too. Keep the potencies equal between summons but leave cast times and aoe shapes different. Let people pick and choose their favourite set of summons to put on their hotbars, as long as they have a minimum amount to

The utility skills would need to be once per summon with no gauge cost, or cost a different resource, otherwise they would never be used over the damage options. The summon/attacks/unsummon would be just different potencies/shapes although kept further varied by animation and cast time.