The freeps does indeed choose a player. All the archery goes onto that persons minions assigned by him.
It can be a double edged sword. In your case Gil it is a blessing.
In my multiplayer games if someone was using archery, the shadow worked together and split the pool so we could play equal numbers of minions as to have overkill on the archery total and leave more minions alive than if 1 guy had played the same amount!