I feel incredibly silly, but I just found out after 2 months of training for the PFT that you can do pull ups pronated or supinated.
I have been doing them pronated (palms facing away) 5 days a week for 2 months. As most of you know, this is way more difficult and I was worried I wouldn't get to twenty before I ship. In the long run, I guess this is a good thing, but man does everything seem a whole lot better with this info!