Could've been giving her to Gortash, who then sets the rest in motion. <...> I was quite surprised that wasn't an option.
I mean, to be fair, I don't think Gortash wants her at that point. Although it could be tied to the whole thing about her being the prototype, I suppose, but why, if what he has now is already an improved version?
Doubly so since he has no way of controlling her, unlike, uh, people in Shadowheart's situation. If you send a non-Origin Karlach in to talk to him alone their dialogue is literally two lines of "prepare to die" variety and then she launches at him. Sure, if you and the artefact go far away enough that she's no longer protected she can become just as much of a tadpoled puppet as many others, but. Let's be honest one of them would be dead before you could go that far.
That's all to say that in this case I am actually not surprised it's not an option. Shadowheart and Astarion are both wanted back and can be controlled (and also have the mental precedent of being controlled before). Gortash doesn't want or need Karlach back, can't control her, never did control her (the only thing he wielded over her is respect, and that's long gone).
Now, Zariel, on the other hand...
Yeah, that's what I meant with "he'll set the rest in motion". He would then continue selling her back to Zariel, while you cement your alliance with Gortash. Maybe in turn he'll give you Duke Ravengard back. That way they wouldn't need to even add any new areas or whatnot, everything's already present in the game.