Conjectural bound for values of Dynkin-diagram friezes

Let a frieze on a Dynkin diagram assign a value to each node. For each cluster, evaluate all cluster variables in that cluster at $1$ to obtain a unitary frieze. For a node, consider the maximal value attained at that node over all unitary friezes.

Unitary-frieze bound conjecture. The value of a frieze at any node of a Dynkin diagram is less than the maximal value of that node over the set of unitary friezes.

The conjecture is needed for the paper's algorithm to enumerate friezes of the sporadic types $E_6$, $E_7$, $E_8$ and $F_4$. Since the set of unitary friezes is computable, the conjecture would provide an effectively computable bound on frieze entries; the source does not state that the bound has been proved.