General-level degree formula for supersingular polynomials

Let $p\geq5$ be prime, let $N\in\mathfrak{S}\setminus\{2\}$, and assume $N\neq p$. Then

General-level degree formula conjecture.

$$\deg ss^{(N*)}_{p}(X)=\frac{(N+1)(p-1)}{24}+\frac18\left(1+\left(\frac{-1}{N}\right)\right)\left(1-\left(\frac{-1}{p}\right)\right)$$ $$+\frac16\left(1+\left(\frac{-3}{N}\right)\right)\left(1-\left(\frac{-3}{p}\right)\right)+\frac12\left(1-\left(\frac{-N}{p}\right)\right)\deg ss_{N}(X).$$

This predicts the degree from elementary residue symbols, the prime-level supersingular degree, and the level-$N$ supersingular polynomial. The source gives no resolution evidence.