In their proof of the Ending Lamination Conjecture, Brock, Canary, and Minsky prove existence of bilipschitz models of hyperbolic 3-manifolds (homeomorphic to a surface times $\mathbb{R}$) depending only on the topology and ending invariants of the manifold.

(See The classification of Kleinian surface groups, II: The Ending Lamination Conjecture and The classification of Kleinian surface groups. I. Models and bounds)

Their proof is non-constructive, so the bilipschitz constants cannot be computed from their proof.

Are the bilipschitz constants close to being computable from their proof? In other words is it "easy" to see what steps in their proof are non-constructive and whether these steps can be made effective?