How to go about More Involved DPS Rotations.

[YusiKha]

Slow on Gravity or... something for Art of War.

A blind for AoW?

WHM

My plan was for Stone/Glare to become more expensive (600-800mp per cast) so that WHM would have more mana issues just going through its nukespam. This would facilitate the need for an on-demand ‘gimme mp!’ button that would also allow you to weave at will (an issue WHM still faces). The addition of essentially Darkside would further push WHM through MP economics questions. Afflatus and Regen’s MP superiority would be much more impactful by reducing the amount of water/osmose casts, even if Cure2/Medica fed the Blood Lily.
WHM would have a safety pick argument in their infinite MP and efficient healing GCD usage. Compared to SCH’s mitigation+shielding, and AST’s larger shields.

SCH

My reasoning was that despite SCH’s past, many/strong DoTs would be better for a GCD focused healer because of their weaker nuke. DoTs could work for SCH, though, if they were the only way to weave without clipping a cast.
Reflecting things like tank busters wouldn’t work as SCH’s damage would differ depending on the encounter. I would like to see Aetherflow moves to a mitigation/damage resource and more emphasis put on the fairy for actually healing.
A way that the counter could work is an AF skill you place on someone with Galvanise. If galvanise breaks before the duration is up, the attacker gets hurt. If catalyse also breaks, the damage increases. (Maybe be able to deploy it too?)

AST

Yeah AST needs something for its mana. Though for the rest of its kit everybody has their own ideas, massively varying. I do want Comet, though.

[Archwizard]

This could be expanded by having held cards giving Malefic an extra effect (maybe MP for Lunar seals, damage for Solar seals, mitigation for Celestial seals?) under the guise of Geomancy spells.

NEXT - DoT Management
We need a 4th healer, and we have 1 GCD focused healer, and 2 oGCD focused healers. DoTs work with GCD healing, and could facilitate a plague doctor, chemist, or biologist type aesthetic.
Multiple DoTs with varying lengths, Thundercloud procs to keep timings variable? Healing GCDs used could contribute to the length or strength of a DoT as a return on the lost damage Spell.

To be honest, I'd much rather see Geomancer added as a full job. With WHM moving away from elemental effects, there's plenty of room for a caster DPS with access to the spells it never used (like Quake, Flood or Tornado).

While SCH's theme is admittedly very muddled, its questline does fir a Plague Doctor aesthetic, and Biolysis is about as close as you can get to biology without introducing science to a fantasy world.
I would like to see more skills oriented around its medical and tactical knowledge rather than its faerie "nurse", but all the same, introducing another job with an overlapping theme would only serve to take away from that.

As for Chemist...
So, an apparently little-known fact is that Yoshi-P admitted in an interview that they originally wanted to introduce Chemist in Heavensward... but could never figure out how to balance the Mix mechanic. For that reason we ended up with AST, whose card system was designed to have results somewhat similar to Mix.
Were CHM to be introduced now, Mix would likely end up as a clone or mix of either NIN Mudras or AST Seals. Either way it would mean a lot of time dedicated to its oGCD skills, meaning a setup more like AST's I'd wager.

Plus let's be honest, we'd get bored of the same three throw animations over an over, and there is a veritable dearth of ideas for mechanics outside of Mix.

4th Healer...
GCD Kit....
Damage over Time.....
DoTs tied to heals or utility in some form...

Combine that with your suggestion change for SCH's Soil and I'd say thats a solid Timemage kit.

AST says hi.
Still has Light Speed, Gravity, Regen and some delayed action effects. Losing one stun doesn't make it less of a Time Mage analogue, and as I said above, introducing a healer with an overlapping theme will not help either of them any.

A blind for AoW?

Possible. I've suggested it before myself.
Personally I'd like to either get some explanation of what Art of War is supposed to be, or just a replacement with something that has more defined thematic elements (cough Miasma 2 cough Meltdown).

My plan was for Stone/Glare to become more expensive (600-800mp per cast) so that WHM would have more mana issues just going through its nukespam.

... which would automatically make attacking less appealing as a White Mage.

Reflecting things like tank busters wouldn’t work as SCH’s damage would differ depending on the encounter.

If the devs found that a real concern, I wouldn't be taking a damage loss as a RDM every time I use Engagement because the arena is too small for Displacement. Besides, as tanks and healers, many abilities are situationally more effective than others, and a damage reflection skill could always have a damage cap.
Bear in mind the devs elected to remove Eye for an Eye, and while they haven't stated a reason, I expect it was partly to make the tank more responsible for their own survivability... and partly because it was just unreliable and not very impactful, since it was RNG on top of a low mitigation percentage.

I do want Comet, though.

Hate to be the bearer of bad news, but between Skyshard, Starstorm and Meteor, caster LBs kinda have Comet covered.