I think I've heard something like if you don't put each screw back in it's original spot, it could make it sag. I think the top screws are a tiny bit different from the bottom ones or something. Not sure, but it's worth a try.
Also, when I changed my cabin air filter, I did it without removing the glovebox. I just laid upside down on the seat and stuck my head under there. I'm short though, so others might not be able to get in there as easily.
Link to understeer.com: