The Moufang property conjecture for strongly transitive compact polygons

Let $\Delta$ be an infinite thick irreducible compact totally disconnected spherical building of rank $2$. Moufang property conjecture. If $\Delta$ is strongly transitive, then $\Delta$ is Moufang. This is the rank-two reduction of the compact building characterization conjecture: connected buildings are already covered by Burns and Spatzier, and the rank at least three case follows from Tits's theorem that thick irreducible spherical buildings are Moufang. The rank-two totally disconnected case remains open in the source.