I'd have to think about it more, but I'm not sure the investigation plan gives us better than 50/50 odds. The mole can just counterclaim one of the real cops. Unless there's some way that we can conclude it's them by forcing them to claim their results first.

Actually I was approaching it as if the everyone claimed both of their results in the endgame. But they have to claim one result the day before.

It seems like the best plan is to no lynch, and force the scummiest people to claim their results first. It still might not be better than straight up lynching though.