I got in not only a cross-saga reference, but a GRRM reference. Score!
From an OOC perspective--
Blackthorn will ensure your loyalty by brute force.
Iulia doesn't care about your ongoing loyalty because she doesn't need it-- by your covenant voting in a block against Blackthorn, you make them your enemies-- which you're unlikely to bear the brunt of without Voluntas' help, unless you're willing to spend sone serious investment of time on the politics game.
Blackthorn or Voluntas, these are the two "I win" buttons.
"Let's try and change the system" is the Hard Way, and by "hard" I mean "bashing our heads against a wall repeatedly to see if the bloody splatters on the wall turn into impressionist art."
Of course, getting PCs to decide what to do is an exercise in herding cats. We see conspiracies where the SG never placed them, miss the ones they do leave clues for and attempt to solve puzzles in ways that the SG never thought of, or had heavily discounted, or in the case he did think about them, they just do it, to heck with the consequences, or even a discussion of risk/reward profiles. I'm constantly reminded of this fact in new, and, umm, exciting ways. Yes, exciting.
That's why I'm spelling out the implications of your options OOC. No one wants to play the politics game, so pick which option sounds best from the player experience standpoint, and your characters can go along with that.
Picking Blackthorn is the option that offers minimal political involvement on your parts. You send one representative to Tribunal with all your sigils, your rep can sleep during proceedings, and vote however Blackthorn votes. Between GF, BT, DF and NS there are enough majority to vote down anything you damn well please. You could probably murder Phessalia in cold blood and get away with it, if you're in the Blackthorn coalition.
Making an enemy of Blackthorn will cause political problems to spring up, which will require allies to deal with, which requires politicking. Iulia will not be your ally, and she will not scratch your backs once she's in power-- but she will be fair.
Phoenix-feather core or gtfo 
Murder Phessalia, hmm? strokes chin thoughtfully (j/k)
Well, you'd have to penetrate. She is, after all, an ice queen.
...Yeah, I went there.
Does this mean that Blackthorn will cause problems if some of Gallus Florensis votes against it but the majority votes for it to retain power?
Heims advocating for Iulia is problematic on multiple levels from a metagame perspective. It may be one of those areas where he has to find some way to vote for Blackthorn IC, because OOC the player can't commit or doesn't want to commit to forging political alliances to protect us from Blackthorn's predation. Whether he gives his sigil to someone else to vote for him, because he can't bring himself to vote for Blackthorn, and can rationalize that by giving his sigil to be cast he's doing the greater good for GF, even though he knows he can't cast the vote himself, I don't know.
The gist of what I'm getting is we need to vote as a bloc as much as we can. I may be reading more into this than Arya intends, which is why I asked the question above.
I don't mind a political saga, I mean I'm running one. I don't have the wherewithal to run one and play one at the same time, so my vote is for Blackthorn and I've made adjustments to my understanding of Tektonius to reflect this. If you guys want a political saga, that's fine, just keep in mind I'll be more on the back burner, and others will have to step up. This is yet another reason why I felt Sophia wasn't getting enough attention from me, and in the end wasn't a good character for me. When Bibracte winds down, and I'm not running a political saga, yeah, sign me up. 
I'm almost certain to have Cygna vote for Blackthorn, too (and why do my fingers keep wanting to type "Blackthron"?), in part because I don't feel up to another heavy-political saga either, and in part because, knowing now what Cygna knows about Iulia and Blackthorn, I can't see her supporting Iulia. But I do agree that we need to vote together in a show of solidarity,eef you weel.
Also, Heims can simply abstain. It's possible that he doesn't like either choice and instead chooses not to choose. 
It's hard for someone to knock an abstention unless it's the sole vote that would decide the matter, of course.
So, voting American-style, then.
No, that's something altogether different. Don't get me started. 
Aww, I see Piper has grown up enough that she can't pretend to be a pretty young boy anymore. No more Peter Pan roles for her. 
Don't hate me because I'm beautiful, baby.
Well, he trust cygna's wisdom, due to his skewed perspective of her as a near-perfect figure (well, he has yet to see her wrong), so she can probably convince him. And anyway, he'd vote with the rest of the covenant, because it's the best for GF, so have no worry.
(Wards are house ruled not to need penetration against creatures with Might, while Aegides dispel other magical effects as normal. ITS the effects dispelled are based on the level of the Aegis rather than on the penetration of the caster(s).)
((So, if I'm understanding right, a Level 20 Aegis dispels any Parma Magica of up to Level 4, not counting Form Bonuses?)
Pardon, I misspoke-- I shouldn't have said that foreign effects were dispelled necessarily. An Aegis resists foreign effects. It doesn't quash them all outright, just the ones that fail to penetrate the aegis.
For the purposes of penetrating an Aegis, I count Parma Magica as a Rego Vim effect which the caster knows formulaically, whose magnitude is equal to the caster's PM skill level. (It's easier to penetrate an aegis with a low level parma, just as it's easier to penetrate with a red dot than it is to penetrate with a Ball of Abysmal Flame.)
So if Aislinn Ex Miscellanea has an 8 Parma Magica, and a ReVi CT of 22 with a score of 5 in penetration, her Parma won't penetrate any foreign aegis, ever. If Aulus Bonisagi has a 2 Parma Magica, and a ReVi CT of 57 with a score of 1 in Penetration, his penetration is 47; he gets to keep his Parma in a foreign aegis up to level 45.
All your parmae were dispelled when you lost your invitations to the aegis; Blackthorn has a level 40 aegis, so your Parma needs 40+ penetration to stay up.
Tabanus: Parma 2. ReVi4, Pen 0. Parma has negative penetration; will be dispelled by any foreign aegis.
Attravere: Parma 5. ReVi22, Pen 3. Parma has 0 penetration; will be dispelled by any foreign aegis.
Sinmore: Parma 2. ReVi9, Pen 3. Parma has 2 penetration; will be dispelled by any foreign aegis.
Iapetus: Parma 2. ReVi0, Pen 2. Parma has negative penetration; will be dispelled by any foreign aegis.
Cygna: Parma 1. ReVi11, Pen 1. Parma has 7 penetration; keeps her Parma in any foreign aegis of level 5 or lower.
Hiems: Parma 8. ReVi22, Pen 3. Parma has negative penetration; will be dispelled by any foreign aegis.
Really dislike how this works and it is completely HR'ed and should be posted there.
Under this framework, I cannot see how NPCs would threaten Wizard's Wars at slight insults as Focus did to Tektonius.
How I choose to calculate its penetration is sonething I came up with on my own, but the necessity of foreign effects needing to penetrate is RAW. Would you prefer to have parmae dispelled unilaterally, than to give magi a chance to maintain them? I'd be fine with that, it's certainly less bookkeeping for me.
Not sure how you're reasoning this should make Focus less of a bully; he's a Vim expert with an assload of Penetration and can walk into most Aegides unaffected. Maybe not Blackthorn's, I'd have to do some math. And in any case Tek had no Aegis to hide behind, either, making how I calculate Parma penetration even less relevant to your stated example.
The Aegis is the foreign effect (to the individual magus), not the Parma. You're reversing it and requiring the Parma to be offensive when counteracting an Aegis and including totals that are completely unrelated to the actual skill. Further, this isn't even disclosed or adequately explained in the HRs. I have no problem with Tektonius's Parma being knocked down, it's a measly 2, and his Vim isn't very high. My problem is that it seems a bit complicated and really wasn't adequately disclosed.
I used Focus as an example not considering his specific specialties. So let me amend it, it makes the only ones who can respond to such insults Vim experts to some degree. I wasn't originally reasoning it based on his Arts, specifically, but just as an example generally. Magi who are not Vim experts won't be quick to drop a Wizard's War declaration under your framework.
My overall point is your HR has a pretty significant cosmological difference from the RAW.