At our school, the university has worked with Google to obtain a large cloud storage solution. I have created a folder and shared with each student. I instruct them to upload their files (large graphic files) in a zipped folder. Then they are to go to Moodle, click on the assignment link and just simply type in the filed that the file(s) have been submitted.
It is not convenient as the files are not in one place in Moodle. But it solves the storage problem.