This is a side-effect of making the king more likely to be good, which I specifically warned people about at the time. I would suggest just reverting that change and going back to 1/3 good, 1/3 evil, 1/3 neutral.
This doesn’t solve everything (as others have said, the evil king usually plays the long con - which means they have to report leads to avoid getting called out by whoever gave it to them, allowing Sheriffs and the like to accuse anonymously.)
But, psychologically, it makes people more reluctant to give their role to the king, and it especially makes the Prince and other vital BD roles less likely to claim to the king, since throwing away their life to get the Prince is a valid and common Evil King play. Making it so that person who didn’t claim could be evil but could also be the prince somewhat decreases the value of making everyone claim.