I noticed that about the Court Wizard, too. I mean, it might be fictionally appropriate, if your gods are foreign gods then you need the move to consult with them.... but mechanically it seems a rough choice.
I'd say to "weapon against throat", yeah you can just kill them outright, unless mitigating circumstances suggest otherwise. I mean, you're clearly not in a FIGHT with someone, right? Fights over, you've won (by achieving the better position).
Re: denied right. Maybe they're accepting the injustice with dignity, because they recognize it's not actually an injustice in this case? Maybe they're forgoing the right in exchange for... acknowledgement of their humility? Or even just self-respect? As an MC if a player did the latter I'd totally be like "Awesome, okay."
I think it's less "I go heal for the rest of the season" and more "Okay, the season passes, what are you all doing? Healing? Yeah, makes sense, probably don't want that wound to be permanent." I mean, if you deliberately want your character to rest and recover BEFORE the "season changes" move comes down from the MC... then say what your character does, and the MC says what happens following their principles and agenda, yeah?