Conjecture on the maximal order of derivatives of the Riemann zeta function

Let $ell\in\mathbb N$ be fixed, and let $T$ tend to infinity. Consider the derivatives of the Riemann zeta function on the line $Re(s)=1$.

Maximal-order conjecture.

$$\max_{T\leq t\leq2T}\left|\zeta^{(\ell)}(1+\mathrm{i}t)\right|\sim Y_{\ell}(\log_2T)^{\ell+1}.$$

The constant $Y_{\ell}$ is not defined in the supplied conjecture span; the surrounding text earlier defines $Y_{\ell}=\int_0^{\infty}u^{\ell}\rho(u)\,du$ using the Dickman function $\rho$. This predicts the precise leading constant for the maximal size of the $ell$th zeta derivative near the $1$-line, beyond the upper bounds described earlier; the supplied text does not specify whether it has been resolved.