Daniel, I'm not sure what part of that seems unconvincing to you. I agree that the leverage is Soleil's life, but I'm not sure why it's all that unreasonable to demand Patriarch take Boiled Face too. Entertoise has the leverage for it, after all. It is threatening to let Tumtum kill Soleil, because that threat is the leverage.
I'm not sure why that isn't sensible. I don't think it's an "out" for Patriarch to take the deal, since that's what Entertoise proposed! That's a success for him. Leverage is Soleil's life, and Entertoise wants Patriarch to either take the deal and both kids, or leave both kids but of his own free will and no hard feelings. On a 10+, Patriarch either takes the deal (great! Now he's stuck with this burden instead of Entertoise) or leaves it (great! Now Entertoise gets to keep Soleil) as per his instinct or personality. On a 7-9, Tumtum can't kill Soleil, because then you have no leverage, but he can certainly start chopping off hands to make it clear he means business. On a 6-, Patriarch says, "fuck you, I can just make more kids. This means war though," or maybe "fine, then neither of us get her," and he kills her himself. Those all seem like they keep AW real while also being a fan of the characters.