Conjecture on the relational complexity of the primitive action of $PGL_2(p)$

Let $p$ be a prime greater than $7$, let $G=PGL_2(p)$, and let $\Omega$ be the permutation domain of the action under consideration. The relational-complexity conjecture asserts that

$$RC(G,\Omega)=4.$$

The claim is motivated by the preceding analysis of $S_4$ actions and the difficulty of classifying all relevant almost independent sets. The case $PGL_2(5)$ is excluded because the paper has already shown that its relational complexity is $2$; the general assertion for primes $p>7$ is presented as conjectural.