To add to/alter your list
Deployment Tactics: Change effect from spreading shields to restoring galvanise effects to full strength and duration, including broken ones.
That would put it in the same niche as Horoscope and Plenary, make it reminiscent of the old Fairy Deploy, and make it a skill worth using outside of raidwide vuln stacks.
Emergency Tactics: Just have it apply a buff so it can be used before or after the shields. Also SCH is not a shield healer, it's just a healer with shields.
Dissipation: Combining a DPS & Healing tool isn't a very wise choice, in my opinion. Especially when it's a long cooldown one, as it will be used on cooldown for the damage portion and the additional healing is just gravy. See Assize and Earthly Star for examples. Assize is the worst of the two, as it has much less leniency in its usage.
If you were to change it, I'd say have it inflict debuffs on the Lily instead of outright removing her. Maybe a healing debuff that Seraph isn't affected by.
Your 'burst damage' idea isn't going to work either, I'm afraid. As healers, we'll need to be ready at the drop of a hat to drop everything and dedicate our GCDs to healing or raising. It'd be straight unfair to pile everything on our cohealer under the guise of 'lol burst phase whatcanyado?'. A more flexible kind of burst could work, like MCH's Hyperdrive and Automaton Summon, but our rotations are already full of 'spam 1 button X times', and we deserve something more than that.
Fey Gauge Actions: If you want to keep these different, and also give SCH an actual 'shield healer' archetype, you could have Eos apply weak barriers with a short duration. If these barriers are broken, a Selene-only healing buff is applied. Selene's Gauge actions would be direct heals made to follow the damage.
(oh btw Eos would totally be the shielder of the two "The sunlight of Eos doth soothe and shield." "The moonlight of Selene doth silence and strengthen.")