Does the Czech sentence mean that we, who are on the stage, cannot hear the actors, who may be anywhere, or that we, who may be anywhere, cannot hear the actors, who are on the stage, or is it ambiguous like the English? The latter meaning is obviously more likely but is the other possible?
It means you cannot hear the actors who are on the stage. It is not really ambiguous.
If you are on stage and cannot hear the actors: Na jevišti neslyšíme herce.
Although there is some small possibility it could mean the other thing when you stress "na jevišti" as opposed to some other place, but I think it would be normally said differently because of the obvious risk of confusion.