Spoiler: About the sins
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I'm not so sure anymore if the seven sins really apply to the demiurges straight away. Please prove me wrong, but if I remember the pages of the comic so far, and also the tumblr account, there has been no word of god, and no straight attribution of the sins to the demiurges, right? Sure, it's mentioned in the wiki (a fan-maintained thing!), and it made totally sense when all we knew were the appearances of the seven at their void concordance. Yet, in-comic, the demiurges themselves have been associated by the author with other things: Their titles, their favorite colors, and the symbols of diamond, sword, tower etc. And if I remember correctly, all attempts of us fans even to sort out the canonical symbols on our own, have failed.

Yep, Solomon comes across as a prideful s-o-b, and he wears royal purple of all things. But I wouldn't bank on his character being ultimately and singularly built around the "Oh I am so pride" trait. After all, Mottom and all her actions are defined by fear, not gluttony - yes, her court has been incredibly wasteful and could be said to be gluttonous. But sloth could also apply to Mottom. Likewise, Mammon is a possessive hoarder, but we have witnessed another side in him. He was haunted by the spirits of his past and future year-end-festivities. In the most recent comic, Mammon and Mottom actually have overcome their "sin" traits if they ever had them.
Next, Incubus. He hasn't been a lustful creep so far, instead he is a scheming dreamwalking creep. Does he satisfy lust in others? Yeaaaah, but "Lust for Success" is really stretching the sin of the flesh into a wholly different topic. If I had to destribute the sins with what we know today, I would say that Incubus and his motives are best defined by envy, not lust.
And we don't even know yet what the deal is with Gog-Agog, Jadis and Jagganoth.


On another note, Solomon appears to have looked for an heir, but so far, he didn't have a prophecy to believe in. With young Zaid now, he has, and he has taken great interest. On the walk to his coliseum, he even explained his reasoning to Zaid. Why should Abbadon waste two whole pages on hypocritic lies?

But, in a way, I think you will be proven right, in a way. Solomon will not step down voluntarily, but only because Zaid is not the true heir. If Zaid would have ten years of training like Allison currently gets, and if Zaid would subsequently beat Solomon in his ridiculous challenge: I think that Solomon would resign, yes. But this is hypothetical. Won't happen. Ever.
My guess is that, when they meet, Solomon will be a misogynist and refuse to accept Allison as true eligible heir of Zoss. If so, you could even read it as "male pride", and be correct in your analysis above.

Now, the current concordance meeting is awkward. Mottom wants revenge from Allison; Mammon wants payback for his tower. Solomon has stolen the false heir, but wants to broker a peace. Incubus and Jagganoth have specifically plotted for the current war and are absent for good reason. Like the absentees, Mottom and Jadis know that Allison is the true heir, so Solomon is lacking vital information. Mammon has been out of the loop a lot, so I wonder how effective he can be in the meeting anyway. Meanwhile, Jadis knows ALL, and can use her knowledge against all the others, but she doesn't strike me as a big schemer. Gog-Agog does, but they don't need to do a thing to get their kick in this situation.

(But also, this is not the most predictable of comics. You can't really guess what happens next - the long-term consequences are usually plain and visible, but not the short-term twists.)