This set of picks from amazon came in a crappy folding zip case so I made a new one.  Not sure it's the best design but it passes the inversion test.

The lid is a sheet of 0.8mm PET (sold as 0.04") cut to ~96x176mm .  I used a tsquare and utility knife, which was quite difficult, so I'd recommend exploring other cutting solutions.  

CAD files included.