Stopple's Z-curve conjecture for zeros of the zeta derivative

Let a Z-curve be one of the level curves described in the source for $\zeta'(s)$, and classify zeros of $\zeta'(s)$ by types $0$, $1$, and $2$. Write a zero as $\rho'=\beta'+i\gamma'$. Stopple's Z-curve conjecture. Asymptotically, $100\%$ of the zeros lying on a Z-curve are type $0$ and satisfy $\beta'>1$.

The conjecture concerns zeros of $\zeta'(s)$ far from the critical line and is motivated by the numerical data, in which all but one of the observed Z-curve zeros were type $0$ and all but $17$ had real part greater than $1$. No proof or disproof is given.