Simply letting the GM also being monarch would be the best way to handle this actually. It's better than having a completely powerless position, since only ceremonial duties don't work well on a forum. Plus constitutional monarchs typically do what the GM theoretically does in making announcements on national policy, etc. even though they obviously aren't able to set it.
It's good to be the king.
I think my first decree will be to put ilikeverin in the Royal Dungeon for 99 years of solitary confinement and hard labor producing sad faces for this forum.