If the owning of a person's soul is shortlisted to either Satan or God, in any of their multitude forms, then that can only be because an individual has sold their soul to one or the other. Either way, it's a pretty raw deal. But that's just my opinion.
Now, if we're to take it that both Satan and God fully exist in your particular story, you could add a little more fiction too. For example, nobody has ever literally been to hell, just as no-one has ever actually been to heaven and brought back proof. At least Walter Raleigh brought a potato back. I would say that a story which questions the ownership of souls should also have some pretty good 'for or against' theological arguments.
And don't forget the atheists. There's a very good chance that your girl, or one of them if you're sending several to hell, will be an atheist. Moreover, she may be an atheist who will never believe in the existence of something without proof. Faced with Satan, she has something which she must grudgingly accept, but if God were to somehow intervene (and I don't mean in the way that people say "That rock nearly fell on her, but God intervened and it missed her by a hair." But if God showed itself, the girl might have to believe in its existence. Which would lead to a quandary; if the once-atheist now believes in both Satan and God because they've both revealed themselves, which one will she accept? Or will she renounce them both, even in light of their existence? In many religious beliefs, atheists don't have a soul, or at least are never going to heaven if they haven't accepted God into their lives before they die. What would happen to an absolute atheist in your story? I would say they could have the power to own their own souls, and not condemn themselves to the fate of either deity.
And let's not leave the pagans out! Take Hel, the Norse goddess of death, ruler of Niflheim, where those who die of 'natural' causes go, while the warriors go to Valhalla. What if your character were a pagan and believed in Hel rather than a christian or jewish form of Satan?
Deep and difficult territory when looked at from all angles.
Just a few thoughts there, most of which have probably completely missed the mark for you. I hope I've added a few more sides to an already very prismatic picture, though.