If the damage of the screws is to big, and you feel that you have absolutely no grip on them anymore, than I would also also try to drill the screwheads off. If you do this carefully with the correct size of drills, you might be able to save the case, This will require the leftover screw ends to stick out a little so that you can still grab them to screw them out. A lot of triwing screwdrivers are poor quality, and a triwing screw already has less surfaces contacting with your screwdriver.
Another thing that might work is warming up the screw with a small tip of a solder iron. If the screw is screwed directly into plastic of the case, the plastic will become weaker and the screw might become looser. The trick is not to heat too much, so that you don't damage your case. (You don't want it to melt together. If the screws are screwed into cupper inserts, this trick won't work. I have no idea how it is with the wii cases. Only loosen the screw, and wait for the plastic to harden again before you fully unscrew it. That way, if you tighten it again, the new screws will still have grip.