You could manage this by setting expectations early. When you start negotiating, a classic trick is to set a few different “packages” and then gently guiding the other side towards the option you really wanted from the start.
So let’s say you really want to do this bit, but you also know management is too cheap; you create a super-cheap option where you don’t do the activity, but something else also happens that management is unwilling to accept, something pretty horrible. Then you have two other packages that are actually desirable, both containing the activity; one of them should be the bells&whistles option that will look expensive. Management will discard the costly choice and the obviously-subpar one, and pick the middle tier. The skill is in not making it too obvious that is what you wanted all along - i.e. you should sound really disappointed that they didn’t pick the super-expensive version.