The critical polynomial conjecture for intervals of length less than four

Let $I$ be an interval. An irreducible polynomial $Q(x)=a_dx^d+\cdots+a_0\in\mathbb{Z}[x]$ with $a_d>0$, all roots in $I$, and $a_d^{-1/d}>t_{\mathbb{Z}}(I)$ is a nonmonic critical polynomial for $I$. Critical polynomial conjecture. Every interval of length less than $4$ has at least one nonmonic critical polynomial.

This is presented as a weaker conjecture that would imply the maximal obstruction conjecture. The supplied text gives no resolution.