It seems that the director should have final say, with a major reason being the cast should only be getting direction from the director. They shouldn't be getting guidance from the producer, playwright, stage manager, or other actors.
I think the issue is he is not just the playwright, he is the primary producer - he is the money.
There are situations where actors get notes from a variety of people - for example, they could be getting notes from a director, a vocal coach, a choreographer and an AD, and a stage manager. So at the end of the day, actors are used to get notes from a variety of people. The issues arise when they get conflicting notes - and at the end of the day, it's the director's job to trump it all.
I was in this situation at a major regional theatre working on a show that was Broadway bound . . . and the playwright had put a bunch of money in it.
In the end, we viewed it as a director/assistant director thing, and moved on. If there ever was a serious disagreement, the two would go off on talk and come up with solution that worked best for them.
I honestly think the director and playwright need to find a way to work together, and not sure if there is anything the Stage Manager can do to make the two play together, other then perhaps initiate a dialogue.
As you continue to move up the ladder of theatre, you will often times work on shows where the director is NOT the person who is the top of the totem pole, and it is a smart SM who learns who the top dog in the production is. (I know of shows where the lead actor were the tall man, and the director hired was just a mouth piece for him. The choreographer was the person who was "directing" the show the most.)
In the end, although it's not ideal, the guy who signs the checks can make the rules.