If you have a large chuck for a vacuum system you can use it instead of a jawed chuck as the jam chuck. Like Mark has written, apply plenty of pressure with the tailstock once you have it centered as best you can.
I have found that taking only a 1/16th of an inch width at a time with the parting tool works well for me. Once it is round, wider light cuts are fine. You may find that shearing cuts across the bottom of the tenon with your bowl gouge are necessary to flatten the tenon. Flatten it and leave a small tenon near the tailstock point that won't interfere with the jaws of the chuck. Leave this small tenon so that you can reverse chuck again later.
You will probably find that the bottom of the bowl near the tenon is warped as well. You must deal with this if the jaws of the chuck will seat against the bottom.