Wouldn’t fix it completely, but it’d be better. You can force every player to enter into an one entrance room one by one to claim, possibly restraining each player beforehand using rope/handcuffs and then forcing them to claim/show known private slots.
Yes, one evil could break this, but then an angry mob would wait outside and since all(?) evils need to break 3 crystals to win as well and some probably need to survive it wouldn’t be safe for them to break this.
I’d be an anti-fun sovereign
What is the desired effect you are trying to get out of a confirmed good starting sovereign?