when you do something different from the player's initial demand and it fails, there should be repercussions - like they currently reduce negotiating mood and raise $$$ demand.
you have to pay for the changes you want. if you short them too much they get offended like like a little prima donna. keep playing around in an throwaway league and stick to some generalizations that you come to from that experience.
i think loyalty and such can influence what you can get away with, but i am not sure at all on that. total assumption. so, going to ignore it for the example.
starting of negotiations: i figure i can knock at least 10-15% off in general. if i have to remove a player option or an early opt-out year that i don't like, i won't reduce it as much or i will meet his $$$ demand and change the other things straight-up. in a very extreme case i may even pay more than their demand.
i don't think it should be an automatic thing that they accept it or even open to it. i can't attest to rate/distribution of results, but from that point of view it's as it should be. i think it's a good thing some players are more rigid than others. i can't apply a one-size fits all method - yet...
in time all is possible, though. unless the metrics used are invisible, it just takes time to find the best way.