Höhn's coinvariant Leech lattice conjecture for semisimple cases

Let $\Lambda$ be the Leech lattice, let $O(\Lambda)$ be its isometry group, and let $\Lambda_g$ denote the sublattice orthogonal to the fixed-point sublattice of $g\in O(\Lambda)$. For a semisimple case in Schellekens' list, let $L_\mathfrak{g}$ be the associated even lattice and write $R(V_{\Lambda_g}^{\hat{g}})$ and $R(V_{L_\mathfrak{g}})$ for the sets of irreducible modules, equipped with their quadratic forms $q$ given by conformal weight modulo $\mathbb{Z}$. Höhn's conjecture. For each semisimple case in Schellekens' list, there exists an isometry $g\in O(\Lambda)$ such that

$$(R(V_{\Lambda_g}^{\hat{g}}),q)\cong (R(V_{L_\mathfrak{g}}),-q)$$

as quadratic spaces. This conjecture proposes that the fusion quadratic space of the orbifold associated with a suitable coinvariant Leech lattice realizes the quadratic space required by the corresponding semisimple case; the source presents it as a proposal, and no resolution is supplied here.