Your reference to sacred values reminded me of Spheres of Justice. In brief, Walzer argues that the best way of describing our morality is by noting which values may not be exchanged for which other values. For example, it is illicit to trade material wealth for political power over others (i.e. bribery is bad). Or trade lives for relief from suffering. But it is permissible to trade within a sphere (money for ice cream) or between some spheres (dowries might be a historical example, but I can't think of a modern one just this moment).

It seems like your post is a mathematical demonstration that I cannot believe the Spheres of Justice argument and also be a utilitarian. Hadn't thought about it that way before.