Conjectural weights of incompressible surfaces in odd pretzel knot complements

Let $K$ be the $(p,q,r)$-pretzel knot, where $p$, $q$, and $r$ are odd integers greater than $1$. The incompressible surfaces in its complement are of Type III or Type II, and their weights are considered in the order corresponding to the trees in the cited figures.

Pretzel-surface weight conjecture. The nine incompressible surfaces have weights, in that order,

$$\frac{1}{2}(p-1)(q-1)(r-1),\quad \frac{1}{2}(r-1),\quad \frac{1}{2}(q-1),\quad \frac{1}{2}(p-1),\quad 1,$$

for the five Type III surfaces, followed by

$$\frac{1}{2}(pqr-1),\quad \frac{1}{2}(qr-1),\quad \frac{1}{2}(pr-1),\quad \frac{1}{2}(pq-1),$$

for the four Type II surfaces.

These weights are conjectural because the paper does not provide a theoretical justification; in particular, it notes that one must verify that all angles can be realized and that conjugate and reducible actions are properly accounted for. The construction is presented as motivation for extending the tree methods from 2-bridge knots to Montesinos knots.