Why not just buy a collet chuck and be done with it all? The collet chuck will serve other funtions as well, like making closed end or kitless pens! To trim a blank square you do what is called facing. You have a few options how to tackle it. You can use a drill press and drill and tube the blank. Or you can just mount the blank between centers and spin it round and straight, then put the round blank in a collet and drill it with the lathe. Either way, you have a tubed blank. You trim the blank with a saw so it's nice and close to the tubes, but not quite there. Then you mount tubed blank between centers and spin it across evenly...this assures the tube is parallel with outside of blank. You stick the blank in a collet so the end barely sticks out..bring up tailstock into hole to help line it up straight in the collet. Then you use your parting tool and part the end of the blank clean with the tube. It makes no difference how big the cylinder is, as long as it fits in a collet you can trim the end really nice and square and the cut is nice and clean, no chipping, lots of control, it's really nice. Before anyone invented all these other ways to make things a bit easier but more to fill their pocket books, this was how it was done, and this is still how many people do things in woodworking. Even the guys that make the huge bowls, the pro turners, they face the bowls on the lathe to add their layers of segments. The brakes on your care are faced square. Makes no difference, metal lathes make this much easier, but wood lathes get the job done just the same. So now you have option 3 !