Superpolynomial-size conjecture for smallest antipalindromic quotient representations

Let $N$ be a natural number for which there exist antipalindromic numbers $A$ and $B$ with $N=A/B$, and measure the size of a solution by the length of the relevant base-$2$ representations. Superpolynomial-size conjecture. The size of a smallest solution to $N=A/B$, if it exists, is not bounded by a polynomial in $N$.

The source discusses computational evidence that smallest antipalindromic solutions can be large, but does not give a polynomial lower-bound theorem or a resolution of the conjecture.