If you are only getting a cup a day, I would quit milking her. Just check her udder daily, if she feels too full clip her to the fence and milk out just enough to relieve her, dip/spray her teats and let her go. You don't really want to bring her back in on the stand as that is a stimulus for milk let down and you don't want her letting down more milk when you are trying to dry them off.
Mine also don't get grain while pregnant until the last month, just alfalfa pellets. Most of mine do get milked until they are 2-3 months bred though so they only have 1-2 months without grain. Their grain is just whole oats, so is really more of a treat while milking than anything else. They get all their nutrients (protein, etc.) from the alfalfa pellets. Mine are also on pasture so they get that too.