All four of the screws on the outside of the case are in WAY too tight and I don't want to strip them.

Hm. Probably the loctite. Using the correct-sized screwdriver head helps, by the way. One of those large-handled screwdrivers with an interchangeable head is often the best way to get those undone. If you use a small "jeweler's" screwdriver set, you might not be able to get enough leverage to undo them.