For WHM, on trash packs you should be using Holy as opposed to DoTing every mob with Aero II—the Aeros just aren’t worth the cast compared to what Holy can do for you. Holy can offer you a Stun for up to 7 seconds before the mobs become immune to it, which means your tank can have a much needed breather when it comes to auto-attacks. It’s excellent mitigation that the other two healers sadly lack. What I tend to do is hardcast the first Holy (tank will have Divine Benison + Regen on him already, or Divine Benison+Regen+Asylum if the pull is relatively large), Swiftcast the second Holy, oGCD heal the tank if need be (usually with Tetra, but sometimes I have to GCD with Solace), and then start casting the third Holy. By the time the third one hits, the mobs will most likely be Stun immune. I keep the tank targeted while I’m Holying so that I can throw heals on them quickly without having to cycle through to find them.
When you have to heal, prioritize your oGCDs first (in this case, Tetra and Benediction); then move to your Afflatus Solace if you have the lilies, since it is instant-cast, and you won’t have to wait for the cast time to go off first for the heal to land. Only after those options are exhausted should you default to Cure II—don’t try to get by with just Cure I. Its potency will be too low during large trash packs to keep up with the incoming damage on your tank. If Divine Benison comes off cooldown and the trash mobs are still alive, throw it back on the tank to add in another buffer while you get another heal off.
It’s also possible that you have landed with tanks that are either pulling too much for their gear, or they aren’t adequately using their cooldowns. Even with heal spamming, you will only be able to hold out so much with the latter type of tank before they bite the dust. And that has always been the case.
For your Esuna, unless the DoT is one that ticks super hard and needs to be cleansed, you can mitigate by just casting Medica II (for party-wide DoTs) or giving a regen (single-target DoT). Take the last boss of the level 73 dungeon: it places a Bleed on the party, but the Bleed doesn’t tick hard enough to warrant 4 Esunas. Instead, a single cast of Medica II will be less casts and less MP cost, and will accomplish the same thing: the HoT negates the DoT.