'I do honestly believe we are worth so much more'............then damned well stand up to them and get what you feel you are worth.
If you saw this through you wouldn't have to keep 'chipping away'.
Get the cake baked, with all the ingredients, this time around according to YOUR recipe, not what French feels he'll deign to concede to you, and from the next negotiation you put the icing on the cake.
Accept this and you'll be forever eating the crumbs management feed you.