Odd rational palindrome quotient conjecture

Let $p>1$ be odd. A rational number $p/q$ has a palindromic quotient representation if there are palindromic numbers $A$ and $B$ such that $p/q=A/B$. Odd rational palindrome quotient conjecture. For every odd number $p>1$ with $p\ne 23$, there exists an odd number $q<p$ such that $p/q=A/B$ has a solution in palindromes $A,B$.

The conjecture is based on the paper’s automaton construction and computational study of rational solutions; the source does not state a proof or resolution.