When that screw decides to pop out, congrats, you've created kind of a sabot round. Somebody's going home with an extra special souvenir!
I suspect without the foamie you are susceptible to slight rollbacks. Chambered ball rolls back a bit, make a little more space for the next ball to start entering the chamber...
I also suspect that the full foamie is not necessary. Just a press fit hard silicone/rubber plug to take up the center space. If it's just a plug, the air might mostly go right past it so it doesn't need to be THAT secure.
I've been meaning to design something and try it out, but I have too many other projects going on.
"Accuracy by aiming."
Definitely not on the A-Team.