I strongly recommend the Southern Shine chip media. It cleans faster and will not get stuck in cases or flash holes.
is there a size on the chips. use a colander kind of thing for separation of pins and brass.
What size/caliber cases are the SS pins getting stuck in??
I have a FA wet tumbler and use their pins, but only load for 204R, 223 & 22/250.
I ... no longer have the issue of brass coming out copper/rose colored from surface zinc loss like I did with Lemi Shine.
Using the SS pins nearly drove me insane when cleaning 6.5 CM brass. They'd stick sideways in the neck, sometime 3 or 4 at at time.
This was a solved problem 7-8 years ago or more. Shorter pins (0.210" long) work in anything 0.224 cal on up, and physically *can't* bridge the neck like you described.
Dunno who you got those pins from, but if it was a reloading supplier they should have known better.