"(I wonder: what, if anything, do you think follows from the lack of any transcendental signified?)"
Isn't that what we are talking about? Semiotic breakdown, no stable anything, nobody can agree on what male or female means, when life begins... anything. Mathematical facts are easy to establish. But agreeing on any kind of common good as a society becomes an increasingly remote prospect, everyone has their own facts. For me, I disregard any source that has ever claimed that men can become pregnant, if they make such an outrageous claim, I can't trust a single other thing they have to say on anything, they've demonstrated their willingness to lie. That doesn't leave many sources of "facts and evidence". God is the ultimate principle, not a man on the moon or a gas. Many people here are railing against a very poor conception of God. Postmodern chaos is not obligatory as you say, it simply is, its what Neitszche understood when he proclaimed the death of God.