Fixed-distance nonsolvability conjecture for maze classes

For each $k$, let $\mathcal{M}_k\subseteq\mathcal{M}$ be the set of mazes whose destination is at distance $k$ from the origin. Fixed-distance nonsolvability conjecture. There exists a $k$ for which $\mathcal{M}_k$ is not solvable. The paper states that this is equivalent to the conjecture that the class of all mazes is not solvable, and leaves it open.