i'll give you a couple tips i picked up years ago working in a plastic machine shop. if your trying to machine uhmw tubing instead of solid rod cut a piece of 1/2" or 3/8 plywood to the same as the i.d. then put in in the end that you clamp in the chuck, all our machines were also fitted wityh 6 jaw chucks.
you'll want to use very sharp hs tools and the trick to parting it off is you must pull the shaving or it will bunch up on top of your partoff tool and break it.
the best way to get a hold of the shaving it to lay your left thumb on top of the partoff tool right before it starts to cut. this will cause the shaving to bunch up on the pad of your thumb where you can easily grab it, then start pulling it out as it cuts.
i would stop trying to part them off at least 2" away from the chuck.