I think you have a fundamental misunderstanding here. You may need to study up what DPI/ LPI/ PPI actually is used for such formats and/ or consult with the actual print facility what they really need. Even if you really, really need those 300 DPI, there are simply technical limitations in file formats or the programs themselves like memory usage or hard-coded restrictions on pixel sizes that may necessit6ate slicing up your artwork into smaller chunks/ strips. Again, even this would be contingent on what the person/ print shop actually doing the reproduction are able to use and what they need, so perhaps that phone call with them will do wonders. Other than that you can always try to rasterize the artwork by importing the AI/ PDF into Photoshop. It has way better memory handling than AI and supports large format pixel images way better.