If you look at the front page you can see that Hippo has posted all the roles in this game. There are no Cult Leaders, "Rogue Townies" or other strange roles.
There is one team of Assasins with probably with about 4 or 5 members, anything else would be a bit unbalanced. The only roles the Town might have are Cops, Docs, Vigs, Masons, Kingmakers and Heros.
Im not saying we lynch someone with complete randomness (obviously with the King there we can't), but its normally a good place to start your votes on.
Hammers regulations sound great in practice except the last one.
Suggestion Three-The King may execute a player if there is direct (investigative, most likely) evidence against that person, even if that person has not reached 33% of the votes
IF all thats needed is an investigation then everyone will claim to have investigated people claiming that they are either innocent or guilty depending on thier motivations.
Might need to rethink that one. 
Could do with a little tweaking so how about this?
Suggestion Three-The King may execute a player if there is direct (investigative, most likely) evidence against that person, even if that person has not reached 33% of the votes as long as the majority of the players trust in that person not bullshitting.
Even if someones motives are bad and they fake a Cop Investigation to get someone lynched, then we can just lynch or vig them as soon as possible.