I've discovered that the capacity for the Cheese Press has been incorrectly set.
By default it allows for 50 Milk to be loaded, but this mod sets the capacity to just 5 (and during testing my Pawns only ever loaded 2 milk into it, and the interface will claim that the cheese press is full despite that).
This makes the cheese press fairly useless for both generating wealth and food, as 16 cheese presses would not be enough to process the milk produced by a single goat each quadrum, so I assume it was an oversight.