After racking my brains for too many days, I decided to go through every setting in the RIP. The software has an option for the white ink that says "Spot color WHITE_INK". I decided to create a spot color in Illustrator called WHITE_INK, and change fill of the eagles head to this color. I saved the file as an EPS, and this made no difference, I then tried it as a PDF, and if printed the head White instead of the dropout. I then tried changing all areas of the image that used white to use WHITE_INK, and it printed fine. The only problem was that using the Spot color WHITE_INK option in the RIP stopped it from printing white underneath all the other areas. I changed the white ink option to "Inked image", and it printed exactly how I wanted.