I was thinking even simpler than that. Hole through the JP, tie a string, tie a big knot on the other end so it doesn't fall down the tube, and done.
I tried the shoving foam down the tube thing, and the two problems I always ran into were:
1) whatever foam I used eventually got packed down and had to be replaced
2) the foam would move around and the shaft/but could get wedged in there. Not a big deal getting it out, but I don't think I'd want my cue with that sort of side force on it for long periods of time if I can avoid it.
In my case, just adding regular JPs was enough to solve the issue for regular cues, but I was fooling around with a jump butt and the string thing worked dandy.