If one examines closely a portion of the emulsion, one can sometimes get a useful clue to the action that will work. Sometimes the more vigorous stirring in the plant setting has suspended small gas bubbles in the droplets of one phase causing them to float rather than settle. These gas droplets can also be associated with some sediment that is suspended therein as well. Application of vacuum to a gently stirred mixture of the emulsion and separated phases can cause these bubbles to break followed by a separation of the phases. This attempt is particularly easy to try in the lab on a 500 ml sample of emulsion from the plant. Just place the filled flask on the rotovap; rotate gently and apply a water aspirator vacuum. Gentle warming is also easy to try out in this configuration. A note of caution should be registered here. You may see a clearing of the emulsion and there is a temptation to take the clarified two-phase mixture and for added safety filter it under vacuum through a pad of Celite. This filtration can undo all the good you have done. Sucking the last of the solvent through the Celite can put gas right back into the phases!The technique of putting a slight bit of vacuum and/gentle stirring and warming on an emulsion can be really helpful. But here's something that Kilomentor mentions that's really key for the beginner -- trying it on a sample.
I don't know what it is about a chemist, but there's a real temptation to try things on full scale first. No matter how big the emulsion is (500 mL, 2 L, 40 L), there's always a temptation to experiment on the actual situation instead of pulling a little off and proving it on a small scale first. (And it's not like I've not been there myself...)