A few issues I see (Sorry if I sound harsh, I have at least got constructive ideas towards the end though <3):

Blanket cool down reductions only works well for healers in the end game when there is literally no opportunity for RNG to creep in under any circumstances. Quickened Aetherflow is the poster child for cooldown reduction done right. There's no RNG whatsoever. As long as you pop those charges, you'll get your 45 second Aetherflow without fail regardless of what you use those charges on. With your rework (And Lilies in general tbh), I can't guarantee I'm going to get the CD reduction, therefore I'm not going to factor it into my plans, therefore the 'Just turn off the Lily Gauge' meme perpetuates onward.

The ability to insta-cast Cure III is interesting, as is the extra 110 overall potency on offer with Tornado. Quake honestly strikes me as the booby trap though. Getting a 3rd Lily from a Shell Proc whilst I'm spamming rocks is likely to get annoying.

Last but certainly not least, Protect and Shell strike me as the worst aspect of this. Moving over to the PvP style of protect is a good concept. Adding RNG in for confession stacks from physical hits on an AoE cooldown literally isn't worth the text string in that tooltip whilst the 50% Lily chance on Shell is just going to be annoying as is.

I don't think the ideas aren't without merit though. IMHO I'd suggest the following adjustments:

Remove the Cast time reduction via Lilies on Cures.
Remove Quake, Tornado gets renamed to Enhanced Aero (bear with me on these).

Switch Protect to a single target 60s cooldown, 10 second duration, 10% damage reduction buff, physical hits guarantee a Lily. Cooldown shared with Shell.

Switch Shell to a party wide 60s cooldown, 10 second duration, 10% damage reduction buff, magical hits guarantee a confession stack. Cooldown shared with Protect.

Excuse the random bolded bits, these details are of paramount importance.

Now for the real meat:

Enhanced Aero II:
Replaces Aero II when you have 3 Lilies. Consumes all Lilies.
Deals wind damage with a potency of 90 to target
Additional Effect: Wind damage over time - Potency: 60- Duration: 21s
Additional Effect: Increases Damage dealt by the nearest player for 6% over the 21s

Enhanced Aero III:
Replaces Aero III when you have 3 Lilies. Consumes all Lilies.
Deals wind damage with a potency of 80 to target
Additional Effect: Wind damage over time - Potency: 50- Duration: 24s
Additional Effect: Increases Damage dealt by the players party by 3% over the 24s

Enhanced Plenary Indulgence:
Replaces Plenary Indulgence when you have 3 Lilies. Consumes all Lilies.
Restores own HP and the HP of all nearby party members. Potency varies with current Confession stack. (150, 300, 450, unchanged from it's current values)
Additional Effect: Resets the duration of all of the players own HoTs upon the target, as well as any Asylum the player may have placed.

The way I see this going, in somewhat optimal play you'll end up generating Lilies through Protect, Regen and Medica II and is still arguably the most up for grabs aspect of the mechanic.

Timing Protect to land during strings of auto attacks and maintaining Regen will be a strong offensive source of Lilies and will combo nicely with the Enhanced Aeros, giving us a weaker but more predictable damage buff vs Balance. Some situations may allow excessive Lily generation which could be used to drop the Enhanced Aero II buff on a couple of people, likely at the expense of personal GCDs. This could be a neat MLG trick, it could end up being worth less than the rocks it cost you doing it or it could be horribly OP. I have no idea =o

Shell is the better defensive cooldown of the two with party wide mitigation and the ability to get a confession stack for Enhanced PI without the need to hard cast a Medica II. This coupled with the HoT reset has the potential to be a useful means of preserving GCDs for more rocks in high end play or those situations where you just don't have anyone worth buffing.

I'm sure my approach is flawed, but it adds some interesting options IMHO.