Rademacher's conjecture for universal coverings of punctured planes

Let $\Gamma\subset\mathbb{C}$ be a discrete subset, let $f:\mathbb{D}\to\mathbb{C}\setminus\Gamma$ be a universal covering map, let $r(f)$ denote the relevant covering radius, and let $f_h$ be the corresponding extremal covering map. Rademacher's conjecture. For every $z\in\mathbb{C}$,

$$\frac{(1-|z|^2)|f'(z)|}{r(f)}\leq |f_h'(0)|.$$

This is presented as a reformulation of the precise-value problem for Landau's constant; the supplied text identifies it as a conjecture and gives no resolution.