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I ran $10^9$ simulations over night and the mean stayed at ~$8.886$. Here's a link of the simulation tallies: wolfr.am/C3YsNZmE. The largest run consisted of 98 lines.
There are 97 more $n < 1000$ for which we know the full factorization of $n!-1$. They can all be found here and here (the lines without a $\texttt C$ in them have a full factorization). All 97 of these do not give solutions.
