See one problem with all this is that
1. The Seven, or at least the more problematic aspects, have deemed us to be worse that the others
2. We have planned to do some significant humbling to the faith.
3. We shouldn't help our enemy till after they stop being such so no building projects
4. Yeah sure a small to medium sept is fine to assuage fears but a grand sept can die in the water
5. Danielle is hopefully reasonable. She would be a fine lever for a schism
All in all while yes I would love to have schism within the faith but I'm not building temples till the schisms reach critical mass.
1. Only the Father has, and to his Chosen only. Whom the Maiden's chosen refers to as an idiot.
2. And this does not run counter to that.
3. This isn't helping our enemy. It's a poisoned gift at best. The Sept is on our land, staffed by clerics chosen and vetted by us, and will be visited by people who came to SD even with all the negative propaganda and then experienced all the good Viserys did. They're not going to buy any calls to action against us, meaning that any Zealot that tries to radicalize will get reported, allowing us to purge SD of hostile elements.
4. The grander the Sept the greater our influence over the Faith. We can't ignore the Seven and it's faithful. Westeros is full of people who worship the Seven and can be swayed by religion. Refusing to engage them on religious grounds will just deliver them on a silver plate to our enemies who will simply decry us as a heretic and demon. You can't rule a continent when the peasants think you're literally Satan. This would only lead to the rise of the Faith Militant, which is a huge mess we don't want. Oldtown has the Starry Sept, King's Landing Baelor's Sept. If we want to justify control over the clergy, then we need a seat that surpasses both so we can move the Conclave to SD once we take Westeros. We don't want them to plot far away from our eyes and hands.
5. Thing is, she won't start or cause a schism on her own. She's the Maiden's chosen, and the Maiden is known to be all about mercy and selflessness. She won't cooperate with us to destroy or take over the Faith for no reason. We can show that we are reasonable and there's a place for the Seven under us as well, if they conform to our laws. Our influence in the faith would then serve as both carrot and strick. Stick because could fracture the faith on our own, and carrot because we could spread the messages her patron actually wants spread thus preventing further chaos.
The Schism is not going to reach critical mass by itself. The clergy are clearly starting to adapt to circumstances. First the High Septon toady get's replaced by someone more zealous (who also just happened to be related to a Reacher Lord), now there's a Council to discuss and interpret theology in light of the coming of magic. Meanwhile, the Chosen have done nothing to confront or truly discredit the clergy, which means that all their acts contribute to the legitimacy of the official Faith, instead of creating an alternative faction, so people will trust the Septons more, instead of less.
Priest: Oh hey this is my interpretation of the Faith
Father in his dreams: Heresy. It is heresy. Also fuck mages
Priest: Wowie thanks Father. I was such a heathen.
That is how I imagine it would go. All I am saying is that first we need to beat them up then we need to pick them up and fix them. I am saying wait not don't do it ever. Like maybe till after we stab the Father in his side and the Warrior too. Fuck that guy.
Peasant: That doesn't sound right. Mages are nice! I'll believe Emperor Viserys, who has done so much good for us, more than some voice in your dreams! It's probably a demon in your head! I'll report you for being possessed!
Inquisitor: Your preaching is against the law. You are hereby expelled from the estate of the Clergy as outline in the Imperial Constitution. Also, you will need to come with us to talk about the voices in your head...
New Priest: Hello! I like mages and think that Emperor Viserys has the Father's Wisdom, the Warrior's Chivalry, the Maiden's Mercy and all the other virtues too!
Peasant: Yay!
That's how I imagine it would go. We have not seen any indication that the Seven are talking to others beyond their Chosen. From the Danelle interlude we even heard that one fey saying that the Father should let his Chosen die and 'roll the bones'. This does not seem indicative that they can talk to as many people as they want.
Waiting until they are beat is foolish. It means conceding the usage of religion as a weapon. If only their narrative about Viserys being a monstrous prevails, then we'll have to deal with a continent full of enemies. By pushing forward our own Septons with Viserys and Imperium-friendly interpretations, we can muddle the waters, making people insecure or outright move them towards our side.
We need to start early so that once the conquest happens we'll have our own infrastructure in place to simply supplant the previous one. We are rising our own Anti-Pope, or Anti-Septon if you want. It'll raise our legitimacy in the eyes of the Westerosi while undermining the one of our religious enemies.