yeah, you need something that will uniformly spin and feed at the same time, as stated above.
a square section (say 1/4") length of steel, heated and twisted (one turn in 16" is common), might form a suitable pattern ? feed it though a square hole, and the rod will twist as it feeds. youd obviously need to attach a sub .177 sized steel rod to the end of it, and the end of that would need your "scratch filing mandrel" or button, or whatever it's called.
Just thinking aloud... something like a giant yankee screwdriver
and yes, definitely pull, not push...
Always looking for any cheap, interesting, knackered "project" guns. Thanks, JB.