Group Caller

I think that to speed along dungeon exploration we should have a “caller” - one player who directs the rest of the group.  Whenever the group enters a room the caller will propose a strategy for examining it.  The other players can agree to the caller’s suggestion or suggest a different strategy if they feel it would be out of character to follow the caller’s suggestion.  As long as there aren’t too many disputes, this would greatly speed things along.  The caller could also direct the group in combat.  You will have to work out the details among yourselves - who will be the caller and what his responsibilities will be.

Remember, even with the caller directing the group, each player has the final say in what his character does and each player will roll the dice for his character.