I put 1 mm thick acoustic foam in, there's plenty of space for more, but I really couldn't tell the difference - the case is very dense, so once you stop any resonance, there's no point in adding more. Frankly, generic cotton wool would work just as well imho, it's just that I could get the acoustic liner free from work. Virtually all the sound is going to come through the front plate, unless you hit the board with the hammer or something - so as long as you can break up the inside surface, you've done all you can practically do - because of the small size you only have to worry about high frequencies (the ping really).
edit - my bad, I measured an off cut, it's ~2mm thick - generic open cell, dense acoustic foam; you can get it by the roll from China. I really doubt you'll get a noticable difference with expensive stuff; but, if someone can prove otherwise - I'd be keen to see your results.