A minimal non-distal system with trivial order-two regional proximal relation

For a topological dynamical system $(X,T)$, let $\textbf{AP}^{[2]}(X,T)$ denote its order-two approximate proximal relation and let $\Delta_X=\\{(x,x):x\in X\\}$. Approximate-proximality conjecture. There is a minimal system $(X,T)$ such that

$$\textbf{AP}^{[2]}(X,T)=\Delta_X$$

and $(X,T)$ is not distal. This asks whether trivial order-two approximate proximality can coexist with failure of distality. The source provides no resolution.