It does, but that can be overcome. As you noted, the secret is to bribe the shit out of the priests.
It’s 50 drachems per point of credibility, plus 10 credibility for having Diakon Edwer when you bribe. “some credibility for your devoutness” is 200, “on the side of the angels” is 300. In other words, I believe I spent about 8000 drachems on the priests (will have to play through again to check), to both boost myself back into the stratosphere and compensate for my heresy and Goety.
NB: My current plan for Alya is the Eclect route, not the Common Voice, and she’s going for a medium Ruthless/Compassionate meter.
I haven’t finished that part of the plan - I have to see what the logistics of the situation are first (and we didn’t have as much information back then - the plan from 2017 is seriously out of date). Tentatively, the first part of the plan is to reduce blood use through Phaedran biotelos and through dropping every Ward except the Erezzan one. If I can’t get rid of Harrowing, I’ll try things like standardizing and raising the age limit, or possibly adopting the Halassurq method (though Alya is seriously 
about natalist policies, because compulsory heterosexuality is heresy. Also, eww, Harrowing children).
Alya does not consider the Cabels her allies. She’s extremely cosmopolitan (they’re homelanders) and generally would rather yeomen not exist (she may re-evaluate this depending on the economics of Phaedran biotelos, but right now she’d rather have helot laborers working on plantations). With that said, one thing she can show is the loyalty of the Rim’s yeomen (because the yeomen love her for stealing and selling their mules and giving them a share of the take - which I’ve jokingly referred to as “socialism” in the past), and if she can prove that she’s protected the interests of Shayard’s yeomen, she might be able to use that as a bridge.
But she really wouldn’t mind having the entire faction serve her in the form of nice little phials of aetherial blood.
In English history, I actually am not finding the examples I thought there were. Mea culpa. Anyway, the idea is that a powerful class of commoners (specifically merchant bourgeoisie) could be harnessed to weaken the power of a feudal class of nobles, as merchants and industrialists have very different needs compared to landowning aristocracy.
If you’re familiar with the Honor Harrington series (which I recommend; it’s kind of Horatio Hornblower in space), one event that happens later on is an alliance between the Commons wing of the Liberal Party and the Centrist-Crown Loyalist coalition, and one of their goals is to break the stranglehold of the House of Lords on politics (in part because Baron High Ridge’s aristocratic coalition is interfering with the defense of Manticore). The Crown of Manticore wants to transfer the power of the purse to the Commons to ensure that another gang of unelected reactionaries doesn’t hamstring the government again.
A historical example might be Napoleon III, who broke the back of the monarchists by being elected on the strength of the French farmers and then launching a coup to kick out the Party of Order.
The Defenders are sounding like one form of a bureaucracy. Either has the issues of watchdogs being captured by the corrupt.
Alya’s own planned countermeasures include, A, being an absolute monarch able to bring down the hammer when necessary, B, targeting the Kryptasts against noble conspiracies, and C, greater inclusion of the merchant class and a nonlandowning officer class in the government and Theurges. As above, this weakens the aristocracy some, but it also means a shift in power and economics away from agriculture. As agriculture is theurgy’s primary economic use, this helps with weaning the Thaumatarchy away from the idea that blood is the only important metric of power, which is part of what’s causing the current system to seize up.
If the Laconniers accept the Xthonic metaphysics of love, and the consequent acceptance of homosexuality and adoption, then yes.
Alya has little patience for the Laconniers either, BTW, and she’ll consider the Leaguers to be useful idiots. You probably figured both of those out already, though. 
Better to light a candle than curse the darkness. If you want there to be light in the setting, then make it yourself.