Maybe we should start from the beginning, and as an example, here is how I personally turn it the second time. I start with a vacuum chuck, but no vacuum, but simply putting the bowl opening over the chuck and the rubber helps spin the uneven inside by friction. The tenon is held in place with a live center. I first true up the top (rim) so that I know where the curve will "exit" the bowls sides. Then I true up the tenon so that I have a plane that is true if I have a bobble (catch) and need to realign the bowl. Then I proceed to turn the sides. Starting at where the bottom of the curve would be on the bowl and at first an unsupported bevel, since the tailstock engagement won't allow it. Then as I proceed up the sides I can rib the bevel. It will take multiple passes to cut supported and clean all the way through the curve up to the rim, once that is clean and true, I sand the outside, Then I can reverse it, and cut the inside, all the way through as you usually will finishing with sanding . After that, I reverse it again on the same vacuum chuck (with vacuum or without vacuum but supported by a live center) to cut off the tenon and cleaning and decorate the bottom, and finally sanding the bottom. So, if you have followed this far, you see I don't use colejaws. You don't have to have a vacuum, but it will make the last step easier, and allow you access to cut all the way across without tailstock and live centers getting in the way.