Isaacs's strengthened conjecture on unitriangular-group character counts

Let $q$ be a power of an odd prime, let $U_n(q)$ be the unitriangular group of degree $n$ over the finite field ${\mathbb F}_q$, and let $N_{n,e}(q)$ denote the number of irreducible characters of $U_n(q)$ with degree $q^e$, for $e\in {\mathbb N}$. Isaacs's conjecture. The functions $N_{n,e}(q)$ are polynomials in $q-1$ with non-negative integral coefficients. This is presented as a strengthened form of Lehrer's conjecture, refining polynomiality in $q$ to polynomiality in $q-1$ with coefficient positivity; the supplied text gives no resolution.