I would lay out and pilot the center on the small end, chuck the large end at tips of jaws realizing you are going to put significant clamping marks into the (large, sacrificial) OD. As has been mentioned, you need to find or make a clamping shoe for the bolt hanging from eccentric locking lever shaft in the tailstock. Otherwise, no way to hold live center into anything. Once you turn your OD (assuming I read it right and you want that) from small end much of the way back down enough to make a clamping area, you need to use a piece of tubing with ID neear your target diameter, better yet take a piece of flat bar and roll it to right diameter, trimming the ends back after you get close. The end gap of your almost complete circle needs to be less than the disance between jaws of your 3 jaw. Turn your part around and clamp the ring to squeeze down on the straight diameter end you already machined. IF you are within tolerance you can work with, you can the use chuck in tailstock to drill a new center in the big end (that should be sticking out of headstock chuck pointing towards tailstock. Now you can complet the OD by turning the rest of the oversize, sacrificial material.