Playing Arkham Horror in a counter-players role as the Herald of the Ancient one or something similar?
To answer the question...the kind of game you're thinking of, really, is Mansion of Madness, which is the Descent version of Arkham Horror.  Players play one of eight investigators and move through a location as they try to uncover a secret plot.  The story teller acts as the Herald or Overlord, by moving monsters to certain locations and playing cards on the player characters as they move through.  Generally speaking, it's very weighted against the players, unless they've played the scenarios a number of times and know what to do in each situation.

What you're proposing is basically the same idea.  Arkham Horror would turn into Mansions of Madness very quickly given the changes you've proposed.  I would say, from the number of times I've retconned certain turns in Arkham Horror, that the game is hard enough with the board being as random and cruel as it is.  If you had someone actively choosing Mythos cards or moving monsters, you would have a much harder and significantly different game on your hands.

My advice to you would be to pick up Mansions of Madness.  It's a long setup for a game, but I like it and what it does to the players as they frantically run around, trying to not die.