Are all Bellamy dendroids non-Suslinian?

Determine whether every Bellamy dendroid—i.e., every smooth plane dendroid whose endpoint set E(X) is connected—is non-Suslinian; equivalently, ascertain whether there exists a Suslinian Bellamy dendroid.

Background

A continuum is Suslinian if it contains no uncountable collection of pairwise-disjoint non-degenerate subcontinua. In smooth plane dendroids, non-Suslinian behavior is characterized by the presence of Cantor sets of arcs. The paper establishes several dichotomies relating endpoint dimension and structure to Suslinian/non-Suslinian properties.

The unresolved point is whether the connectedness of the endpoint set in a Bellamy dendroid inherently forces non-Suslinian behavior, or whether a counterexample exists in the form of a Suslinian Bellamy dendroid.