I skipped the build part and jumped to the testing phase. I immediately saw where it could be improved. One, the hopper needs to be built like a dice tower so the weight of the NERF balls doesn't cause a jamb. Second, the gun should be harness mounted like in Aliens.
http://thenerdybird.com/wp-content/uploads/2016/04/AliensVasquez4.gif
https://youtu.be/G7MDrUG4cws?t=33m