I love negotiations, and the battles that follow when one party has been clueless for ages, and insists that they get their way or WAAAAAHHHHHHHH. Of course, you don't fall into the WAAAAAAAAHHHHHHHHH category spellcaster. I just think it's really humorous when a major national corporation has absolutely no real power to make you stay. To demonstrate, I'll list the major sources of power:
Retribution
Reward
Reverence
If they can't reward you, punish you, or gain your awe, they have no power over you. But, you have the power of Reward or Retribution (help them out, or let them suffer). Tell them to **** off.
You know they need you more than you need them. Just make sure you don't fear the consequences, and you can either make your demands just as radical until the managers inform the honchos what idiots they are, and they cave; or just say no. You did a good job in saying that the matter is out of the question, because that's the only way to really make it clear that you're done negotiating until they get some power. Just hope that they don't get any retribution power over you. :p Good luck dealing with them