Obviously rather late to the party here, but . . . . . . . .
If he manages to figure it out, isn't the sane response to go "Oh. Oh well." and keep living this life? The devil didn't set any time limit, after all, and she can't read his mind - if he never tells her he figured it out the game will never end.
I mean, it'll end up eating at him constantly, and maybe that's the point - maybe that's the kind of thing that would end up pushing him over the line between human and devil. But his sister would get to live, his family would get to live a life that didn't include her death, and given he was willing to die himself to avoid losing his love for his sister I expect he'd be okay with that trade.