...So why can't we ask for the same consideration? "We think we see a way to save some money, what do you think" - that sort of thing. is there NO room for negotiation here?

No, not in my mind.

He was awarded the contract fair and square then you changed the requirements. You asked for the net cost for the changes and you don't like them. These costs were calculated using the same method used to determine the original cost. Now you want him to negotiate. Why should he? It's like telling the lowest bidder "you are the lowest but you will have to do better".

Sounds like you know you have this guy over a barrel and are using this opportunity to get a better price.