H-principle for corank two distributions of odd rank and maximal first Kronecker index

We study corank-two distributions $D$ of odd rank $2N+1$ whose associated pencil of skew-symmetric forms $\{dα|_{D}(q)\mid α\inΩ^1(M),\ α|_{D}=0\}$ lies, at every point, in the generic orbit of the natural $\mathrm{GL}\bigl(D(q)\bigr)$-action; equivalently, $D$ has maximal first Kronecker index. In