I'll just add: to estmiate stuff like BATNA, try breaking the problem down and summing up. It's the same as in programming. How do you solve big problems? By breaking them down into littler and littler problems.

Then when you go back to talk to these folks, give them the rationale and the small numbers rather than (just) the big number. If they have issues with your methodology you can likely work it out.

This is largely covered by the book, "Getting to Yes". Short and helpful.