Thank you all for your comments people! I was a little nervous about this post but it seems it's starting to spark an interesting discussion. I'll try to tackle the various points that have come up by making a summary of them — I'm not going to quote or I'll end up making another 100k words post lol Feel free to bonk me in case I've forgotten something y'all thought was important.

1) No matter what you do, people are going to be unhappy about Summoner.
This saddens me a little and I strongly disagree. Sure, a perfect solution that has a 100% success rate is highly improbable, but I feel like the greatest obstacle in satisfying most people lies not with SMN itself, but rather the absolute alternative between old and new that has been forced on us: old Summoner OR new Summoner — the fact that different people can't freely pick what to enjoy is the core issue. And why is this alternative a thing in the first place? Because SE elected to completely erase an entire job and play style which (with highs and lows ofc) had been going on for years and years and was liked by many... not by everyone perhaps, but that is inconsequential. You just DON'T delete something so rich and with such an history to please people, especially when a better crowd-pleasing alternative exists — and believe me, if even I could think of it, the solution really is simple.
It also feels like a kick in Thal's b4lls that they would remove the pet DPS in an expansion which somewhat fixed the responsiveness of pets.

2) What would become of the relationship between ACN, SMN and SCH?
I hope I don't really have to confirm that I am aware Arcanist is the base class for the Summoner Job lol The whole post I wrote is precisely about that fact and why it's not good. The supposed 1.0 coding issue can probably be worked around as the only big thing required would be an additional "Arcanist-specific Job stone" to replace the Summoner one, which should now be treated as independent. Assuming we're in an ideal world where coding issues are not a big deal, I'd say the absolute best situation would be: a) Keep ACN as a class and upgrade it to an independent Job at 30 — you can call it however you want really, as long as the kit stays the same; b) Make SCH accessible from level 1, so people have two starting healers; c) Make SMN an independent "unlock-at-30" Job like AST, DRK and MCH.
In a NON ideal world however, the easiest route would be to just have all three paths branch from the base Arcanist and pretend you don't see half your buttons change/disappear when you equip a different job stone (this didn't seem to be a problem for SE in ShB, considering the desolation you experienced when you unlocked Scholar).
I'm under the impression that "the class-job system being too ingrained in the game" doesn't really constitute a substantial obstacle. Probably the most "annoying" part would be to create a couple of new job-related quests and a bunch of extra dialogue... if they really want to — it's not even mandatory tbh and people who just want to enjoy the job wouldn't even care.

3) What about Equipment?
I'd say just let this new-Arcanist share its Equipment with Summoner. Sure, you end up getting three book-wielding Jobs but... is that really such an issue? To quote a commonly used sentence in these Forums: "If you don't like books, go play something else gné gné" xD I mean, we have all kinds of swords and canes everywhere and I don't see people complaining. Heck: for the sake of simplicity you can even make them share Relic Weapons without much of a problem. The only thing that would be missing still is Artifact Gear sets for new-Arcanist but once again this is just something extra which I can freely do away with as long as I get to play with the old toolkit... and I'm sure all the Nier-glamouring catgirls would agree with me that this is not such an important aspect.

4) New Contagion is too much like NIN buff and that's dangerous.
Mmmh, point taken. I wanted to make something different from a generic party-wide damage buff especially since Summoner would still have its own Searing Light. I'll try to see if something that is still somewhat different comes to my mind, but I guess options in this regard are really limited at the end of the day.