frank,

we take risks every day. why would you want to give up any reward?

just go with the fixed price and reap all the reward, or go straight T&M and release all the risk.

with your scenerio, you are still taking all the risk, but only reaping part of the reward. The customer releases all risk, but still reaps some of the reward.

Because in your scenerio, if it comes out to $1100, does the customer split your loss with you?

so why split your gains with them?