There's no real reason why a "DoT" is necessary. It's not "Preferable" for a healer in any way.
Whether you have a 50 potency DoT lasting 24s or a 400 potency direct damage nuke, the outcome is still the same. Spending one GCD on 400 potency spell. (The only difference is a DoT you want to snapshot with damage up buffs only, while a direct damage skill you want to use while under damage up buffs as well as benefiting from debuffs better)
Anyway, as far as I'd make Quake/Tornado work...
I'd probably do something like:
Tornado: Deal damage to target with potency of 300 and deals 50% damage to targets around them. Costs 3 Lilies.
Bonus effect: Deals 150 potency more damage for each of your Aero spells active on the main target.
Cooldown: 30s
Quake: Deal 200 potency damage to your target and all targets near them. Costs 3 Lilies.
Cooldown: 15s
Which is why there must needs be a mechanic that is not focused around Cure usage.
No generation of Lilies from Cures, no expending of Lilies through Cures. DON'T USE A MECHANIC THAT WANTS US TO USE THE SKILLS WE NEVER WANT TO USE.
Make Lilies work with literally any other skills in the WHM kit. Anything other than the 2 spells we don't want to use unless it's REALLY necessary.
Some suggestions for Lilly generation and effects that are nothing to do with Cure:
Regen ticks have a 20% (100% if critical) chance to generate a Lily.
Casting Stone on a target that has one of your Aero effects on them has a 20% chance to generate a Lily. This chance increases to 40% if both Aero effects are on the target.
Aero DoT ticks have a 20% (100% if critical) chance to generate a Lily.
Lilies can be spent to cast Tornado or Quake.
Lilies can be consumed by oGCD heal skills (Asylum, Assize, Tetra, DB) to reduce all active CD's by 1/3/5 seconds.
CURES ARE NEVER EFFICIENT.
Whether you spend 2s casting Cure I/II or 0s casting Cure I/II you will still need to wait out the 2.5s GCD before you can start casting another GCD skill.
Making spells instant does not suddenly make them not use a GCD, otherwise RDM's would be broken and Swiftcast would be used to weave extra Stones/Aero III's into your rotation.