The way I can see to add complexity to it without falling into the same trap as all the other jobs (utterly static rotation, all just finger-busywork) would be to:

1. Define 3 "types" of summons, one for each gem. Say the first gem is always slow casts but very high DPS. This is your damage summon. This is when you deal the damage of your minor phase, it should account for ~50% of the total damage. The second gem is about mobility. Either all-instant, or some form of movement ability. The third gem would be utility. This could be a host of things, usually it's some form of personal defense or group utility.
2. Rebalance the current summons to fit this pattern. This is somewhat easy, as they're surprisingly close to this already: Beef up Ifrit's damage massively. Reduce Titan's damage to compensate. Titan becomes the mobility summon, Garuda gains a 1.0s cast time on the nuke to reflect this. Slipstream takes from PvP, giving group movement speed while inside its - now larger but not infinite! - radius, in turn its tick damage is reduced.
3. Add at least one extra set, say Ramuh + Leviathan + Shiva (ordered to reflect Ifrit + Titan + Garuda). Same roles, different mechanics! This set is themed "all AoE", the two buttons do the same.
4. Ramuh has a single channel cast. While you channel, lightning bolts keep rapidly raining down in a radius around your target, preferring the main target but hitting around it, too. You can walk while channeling like PvP casts, but you cannot in any way about it, and it lasts 4 GCDs. Again the high-risk-high-damage idea. His "utility" is a 2.5s cast single hit large lightning bolt that grants a Ruin IV charge. Leviathan has line AoEs that are instant cast but have a relatively slow animation as the wave rolls through, his utility is a really wide version of this that has a very short cast however. Shiva as the utility summon is a debuff type: The 5 charges of the very low damage forward cone AoE slowly apply a stacking debuff. The higher, the less damage that target deals to you. The utility ability has no limit, but by itself deals no damage. It removes the debuffs, dealing damage, and if at 5 stacks applies a new debuff that heavily reduces damage to the summoner for the single next damage deal to them.
5. Importantly: Which set you get is random. You need to react mid-fight to what happens, you can't pre-plan your combat.