I would have something to offer but I think SD put it well.
Banks generally will do the math.
If they think they can net more as an REO, then they will. Sometimes they can. Often there are variables at play that you cannot decipher. For example, if their mortgage insurance only kicks in if there is a trustee sale, they might be willing to go a lot lower on the market value of an reo.
Bottomline, you really need to define your variables and play your game. If you spend your time trying to bluff them and end up losing something dear (money or a favorite home) you will end up with regret. Focus on what is most important here and act accordingly.