It's alright to say, 'to get the best out of the actors/actresses.' Can we also say, 'to get the best play out of them.'? (This is what a director can manage of course!)
My feeling is that I might expect to hear one of three utterances, none of them containing the word 'play':
1. The director hopes/wants /is trying to get the best performances out of them. = the best display of acting skills.
2. The director hopes/wants /is trying to get the best production out of them. = the best production of the play staged.
3. The director hopes/wants /is trying to get the best performance out of them. Context would tell us whether meaning #1 or #2 was implied.
I stress that this is only my feeling. I also feel that if we want give the meaning of #2, the suggestion I made above is clear:
... to get the best play on Broadway out of them.
I think the reason I too would be unlikely to say "get the best play out of them" is that what comes from actors is not the "play" - that comes from the writer. I think that a viable sentence would be:
"The producer worked closely with the writer to get the best possible play out of him."
Actors don't give you a play, they give you a performance. I wouldn't even say they gave you a production, as fivejedjon rather tentatively offered as an alternative. I think a "production" would imply not just actors but also designers, crew and indeed the director himself - it's more of an overall thing, not just down to the actors.
I think performance is the most natural choice of word here.