The collinearity conjecture for polynomial Heun eigenfunction points

For $l\in\mathbb N$, let $\mathcal P_l\in\{B=l\omega\}$ be the point with maximal $A$-coordinate for which the corresponding Heun equation has a polynomial solution. Collinearity conjecture. All points $\mathcal P_l$ lie on the same line. This is an observed geometric pattern for the parameter points associated with polynomial Heun solutions; the source provides no resolution.