So, I did some more research and learned that WD 40 is NOT what to use. We did not take the press apart, but cleaned every surface carefully with compressed air and soft cotton, and then oiled her thoroughly with 30 weight oil. The press looks great!
My husband is not willing to share his garage with me so we are creating an interim space for the shop and are already developing designs for the future in our heads. Amazing how exciting this is. 🙂