The Orbifold Mordell Conjecture for orbifold curves

Let $(X,\Delta)$ be a smooth proper orbifold curve over a number field $K$, where $\Delta=\sum_i(1-\frac{1}{m_i})D_i$, and call $(X,\Delta)$ Mordellic if, after every finite field extension and for every regular finitely generated integral model, the set of orbifold maps from the model's base is finite. Orbifold Mordell Conjecture. If $(X,\Delta)$ is of general type, then $(X,\Delta)$ is Mordellic. The conjecture is open for every general-type orbifold curve whose boundary has only finite multiplicities and whose underlying curve has genus at most one.