FUCK, FINALLY GOT THIS SONBITCH!
Vorp's idea to use an array within each object helped me do the sorting methods with a breeze, so the array was technically never altered. However, the names and CORRECT scores kept coming up in different places (which, again, wasn't a problem) so I needed a way to fix that; here I just made a recycle method to take a copy I made of the original array and reassign all the elements. This damn simple concept took me far too long to code, but I thank everyone for their help.
Here are the urls again with the final project.
http://www.georgiasouthern.edu/~joxford1/Tests.java http://www.georgiasouthern.edu/~joxford1/Student.java