I have figured out how to do it.
1. Go to the Control Center in KDE
2. Enter the System Administration category
3. Enter the Paths subcategory.
4. Enter a different path for the desktop. You may be asked to move the existing files to the new location.
5. Now head over to GNOME and you will be able to choose different icons.
I'm still having a bit of difficulty with another problem however, and I cannot figure out this one. When booting to KDE after using GNOME, all files open with whatever they open with in GNOME until I go to the file types section of the control center, and just hit ok without changing anything. Then the problem goes away, until I boot to GNOME again. It's really not too bad, because it's easy to fix, but it would still be nice if I could somehow get rid of the problem perminently.