I ended up taking a simple pieces of transparent tape and sticking them along both sides of the MDA about the length of the display. You can cut the tape once its in place with a sharp razor blade. When its done well, you won't be able to see the tape once its fixed. I used TESA, but I'm sure it doesn't matter what kind as long as it is really transparent. Wouldn't try Scothtape though, as its also quite slippery.
Best thing now: I can finally get the gripp of my MDA! On the next one I'll do this right away and avoid the scrathes mine now has from falling on the floor.