Remember to extra nice to the person on the phone. They are not use to it and you will get a lot further. It is negotiation. There tatic is to tell you that and if you get them current then they call it a win.
So the question is, how much would it take to get the second current? It might be worth doing, or offer them half of that.
Have you tried talking to the department head? I have never completed a short sale with Household Finance, I believe that you may be talking to the wrong people as well. Keep asking for their superior. See if that gets you anywhere.