Critical Restricted Sumsets at the Boundary $\lvert A\rvert+\lvert B\rvert=p$

Let $p$ be an odd prime, and write $A\RS B=\{a+b:a\in A,\ b\in B,\ a\ne b\}$. We classify all pairs $A,B\subseteq\Fp$ satisfying $|A|+|B|=p$, $|A|>|B|=\ell\ge1$, and $|A\RS B|=p-2$. After normalizing the two missing sums to $\{0,1\}$, we obtain exactly $\ell+1$ explicit models. The classification fo