Sloane’s conjecture on multiplicative digital root

It is believed that there is no integer has a multiplicative persistence greater than itself, a conjecture put forth in 1973 by Neil Sloane, and that Sloane meant to limit this conjecture to fixed radix bases.

In 1998, Diamond and Reidpath published a factorial base counterexample, by proving that “it is possible to find a number in factorial base of arbitrarily large persistence,” specifically a number of the form

$$n!n+\sum _{i=1}^{n-1}i!$$

Obviously, this number will have a factorial base multiplicative digital root of $n$ and a persistence of also $n$, suggesting an upper bound for the desired counterexample.