Motivated by our search for a representation-theoretic avatar for double Grothendieck polynomials, we give a new formula for these polynomials based on Magyar's orthodontia algorithm for diagrams. We obtain a similar formula for double Schubert polynomials, and a curious positivity result: the polynomial $x_1^n \dots x_n^n \mathfrak S_w(x_n^{-1}, \dots, x_1^{-1}; 1, \dots, 1)$ is a graded nonnegative sum of Lascoux polynomials. Joint work with Avery St. Dizier.