  Arguin, Dubach & Hartung recently conjectured that an intermediate regime
exists between IID and log-correlated statistics for extreme values of a random
model of the Riemann zeta function. For the same model, we prove a matching
upper and lower tail for the distribution of its maximum. This tail
interpolates between that of the two aforementioned regimes. We apply the
result to yield a new sharp estimate on moments over short intervals,
generalizing a result by Harper. In particular, we observe a hybrid regime for
moments with a distinctive transition to the IID regime for intervals of length
larger than $\exp(\sqrt{\log \log T})$.
