I'm talking about the light arts side of it. Which, from my understanding, people /WHM for.
Wrong.

I'm pretty sure SCH gets access to the same refresh gear WHM does, excluding Orison Bliuad +2. I don't know if SCH empyrean body has refresh. I know there's the WOTG earring, Wivre Hairpin is any job, pretty sure Stearc subligar was any job, Owleyes. Am I missing anything? Then if you're going to throw in Refresh II and ballads, same could be said of SCH. But in cases where there isn't refresh II or ballads, SCH has this refresh gear and a better sublimation.
In said cases, SCH would be main healer? Well let me drone on back to why WHM is better. SCH will pull hate. If you haven't got a BRD and RDM (though RDM is largely ignorable), chances our your DDs aren't going to be killing quite as fast as they should be and I can only have flash backs of the horrors of main healing tanks without March. SCH having to Cure bomb with a spell that generates more hate than Cure VI doesn't last as long as it needs to in such a situation, which is why you bring a WHM. Hell, even when SCH did outclass WHM and BLM, both were still common place, if not vital (I never remember not seeing both jobs in Alliances) and that was before SE decided every job but SCH should play a part in making stuff drop.

As far as Aminus Minuo, I'm sure you can find the right set of gear that has a good balance of cure potency, -enmity and MND. I know my friend had a good one. I'll have to ask her what it was. Or put one together myself. Aminus Minuo is 1 to 2 less slots taking -ENM in gear.
You've completely missed the point. WHM still generates vastly last enmity than SCH. SCH gaining more hate with Cure V doesn't change that (well actually it does, but it's a negative change on SCH, go figure). Animus Minuo doesn't do squat, both jobs can probably already cap out -enmity, it's a worthless spell.

Breaking Rapture in a good way. Like, making the recast 3 minutes, or something that is nearly on the verge of being unbalanced.
Wait, so not only do you want SCH to be able to cast the same level of Cure as any /WHM job, but you want to put the only thing that redeems SCH healing on a 3 minute timer? Get the fuck out of this thread. Now.