I do nearly the identical job with the same dimensions. One difference is that I use a larger more rigid lathe that has never had any difficulty parting anything. I see many posts regarding parting problems using smaller lathes, so there may be issues there.
I have a shouldered (OD smaller than the tube OD) plug that fits snugly in one end of the tube so the chick jaws have something to grip against and not distort the tube. I also use a six jaw, but would use soft jaws if I didn't. The far end gets a similar plug that has been center drilled. The tube is chucked and the tailstock with a live center used. The key is not to have any real pressure on the tailstock center. I snug up the tailstock in the normal fashion when tightening the chuck jaws, but then release the tension after that. I then start the spindle and rest my finger on the live center and adjust the tension until the center just starts spinning with the part, no tighter. By using minimum tension the parting blade does not get pinched when it cuts through. I do all of this with just saw cut ends that are close to square. Next I make a parting cut about a quarter inch from the tailstock end to get a nice square end on the tube. Then the tube is reversed in the spindle and the whole process done again. Now you have nicely machined square ends on the tube and you can start parting off the 1.5" sections from the headstock end moving the plug with each cut. I have done it by parting then off from the tailstock end as well, but you may be better off parting close to the chuck.
The whole key is not to have tension on the live center causing the parting tool to bind in the cut.
I hesitate to post this as it is sort of a finesse job, but with care and proper lube (flood coolant), I have parted off many rings, but as I stated my lathe is fairly stout. I have a 12" bench late as well, but have never tried using it for this job.
It all depends on finesse and having a bit of lathe experience, so be very careful, as if the parting tool grabs, it won't be pretty!
