In 2019, Dimitrov proved the Schinzel-Zassenhaus Conjecture. Harry Schmidt and I showed how his general strategy can be adapted to cover some dynamical variants of this conjecture. One common tool in both results is Dubinin's Theorem on the transfinite diameter of hedgehogs. Motivated by Mahler's work on root separation, I gave an elementary proof of Dubinin's Theorem, albeit with a worse numerical constant. In this talk, I will report on joint work in progress with Harry Schmidt. We find new upper bounds for the transfinite diameter of some finite topological trees. We construct these trees using the Hubbard tree of a post-critically finite map. They are more attuned to the dynamical setting than hedgehogs. As a consequence, we can cover new cases of the dynamical Schinzel--Zassenhaus Conjecture.