Cool idea. I tried wood dowels but it usually broke apart.
I've come up with an idea of a spring loaded take down tool. Never have built it. Shouldn't cost much and won't be big. My Bushmasters aren't much trouble to push out with my fingers. But my other carbine built on the RRA receiver is a pain in the ass.
ETA: Here's my idea. Excuse the crudeness with no measurements or details. First time I ever took it out of my idea and actually put it out. Basically some sort of tubing or pipe. 1 rod all the way through. Either bend at a 90 at the back, add a "T" or leave it alone. Weld a washer that does double duty as a stopper and spring cup inside the pipe/tubing/cylinder. Use washers as end caps.
The only real issue would be if you miss with the punch part of it and pop your receiver.....