Upper bound for categorifiable near-group fusion rings over cyclic prime groups

Let $C_p$ be the cyclic group of prime order $p$, let $R(C_p,\ell)$ be the near-group fusion ring with group of invertible elements $C_p$ and parameter $\ell$, and call it categorifiable if it is realized as the Grothendieck ring of a fusion category. Upper-bound conjecture. If $p\in\mathbb{Z}_{\geq2}$ is prime and $\ell\in\mathbb{Z}_{\geq0}$, then

$$R(C_p,\ell)\text{ categorifiable}\quad\Longrightarrow\quad \ell<p^2.$$

This is presented as a conjectural restriction on the possible parameters for categorifiable near-group fusion rings. The supplied text gives no resolution status, so the bound remains open here.