How to go about More Involved DPS Rotations.

[Archwizard]

With regards to creating more complexity with Healer DPS rotations, this big thing isn't necessarily in "how" to do it, but rather in how "much" to do it. Bear in mind that regardless of the number of buttons you're hitting, you will ideally do less damage than any DPS on the team (not simply for balance reasons, but so the overall rDPS loss when you stop to heal isn't bigger than letting your lowest DPS die).
Set up too high of a skill hurdle for too little of a reward, and you end up with extremely busy yet low-performing jobs like Ninja.

So, I would like to propose thus:

1) Tie some elements of the healing side of the kit into their core DPS rotation.
There are multiple ways to go about this.
The most direct route would be to follow the example of White Mage's Holy skill, which inflicts a brief but potent detriment on enemies it affects, drastically increasing the tank's survival for a brief period through the healer's direct intervention. You could give similar tools to SCH and AST's respective AoEs, like a Slow on Gravity or... something for Art of War. Or to be less derivative, have Broil inflict damage down (by aiming at the target's weaponry), Glare inflict Blind, or Combust curse the target somehow.
Alternately, as OP notes, another aspect of this could be having DPS abilities for resource management. Cast Stone/Glare to speed up Lilies, cast Malefic to regain MP, cast Broil to speed up CDs or drum up procs, etc.
All of the above provide tools where even though you're not directly healing, it doesn't mean you're not contributing to healing or survivability in some way, so nobody is allowed to complain you shot the boss instead of throwing them a Cure. (They'll do it anyway, but this way you can say "I needed MP" or "I just saved your life and got more out of that than a Cure but go off".)

2) Create high-risk, high-reward DPS tools for each healer.
I don't just mean "high risk" in the same way getting greedy with a Stone/Glare means more hits on the tank. I mean have potent DPS tools that actively compete with the healing tools you have within the kit.
For instance, having a damage skill that consumes Lilies as a White Mage -- you're consuming resources that are used for potent and expensive healing in order to dole out more damage. You could do the same thing for SCH or AST by having damage skills that share CDs with their healing oGCDs, creating scarcity to encourage the use of their GCD heals.
Alternatively, giving a "Cosmic Alignment" buff to AST or "Press the Advantage" to SCH that increases their damage slightly but cripples their healing until it ends, like the old old old Cleric Stance.
Why? Because this way you can set your own skill ceiling by choosing how cautiously you want to play.

3) Give back the ability to spread DoTs in AoE.
Fairly self explanatory. Our AoE rotations consist either of spamming one attack and maybe a CD, or manually multidotting. The former is even more boring and the latter is painful, especially in the case where you have to heal the tank between casts.
You could even give healers abilities that have the Thunder 2/4 treatment, where they're mutually exclusive with other DoTs. Point is, let them spread so we have more to do and less time wasted doing it.

Now, that being said, I have some different ideas than OP as to the "how" for existing healers.

WHM: The last thing our lovely mage needs is more MP recovery. At present between Lily heals, Thin Air and oGCD heals, it's so good at eliminating costs that I can press LD maybe once per fight if I'm playing badly.
That said, I'm not entirely sure what WHM could use. A Lily spender to attack with? Another oGCD attack?

SCH: To the contrary, I actually think we're ignoring that SCH once WAS the DoT-focused attacker amongst our healers, until all Miasma effects, Shadowflare and Bane were removed from its kit. Most were fire-and-forget, but you still had to manage with an extra DoT and without SMN's Tri-Disaster.
I would almost be willing to suggest a proc of some sort as well for Ruin II, though that would just piggyback off of Ruin IV for SMN.
I could also suggest throwing some counter-attack effects on the tank -- sort of like Eye for an Eye, but more literal Spikes effects or even straight-up Reflect, use tactically and time the cast perfectly to slap a boss in the face with its own tankbuster.

AST: Meanwhile, this is the perfect repository for self-buffing skills. Alternately, for damage buffs in general; I have half a mind to say AST's damage contribution should largely come from the time spent applying buffs to higher DPS individuals. Of course that would be no less boring, exhausting, and unhelpful for solo content.
Funnily enough, AST is also the healer I would say is most in need of MP management skills, especially with the losses of Ewer and Lady of Crowns.

Personally with regards to a fourth healer... I admit I'm biased since I have tried to push Necromancer as a battle healer, but at the same time, I think having the devs work on a job whose kit is "deal damage in order to heal" might give them some needed perspective on the damage tools available to other healers, much as working on Gunbreaker gave them perspective on how to balance existing tanks.