Handles are something I agonized over for quite a while, till I figured out a simple way to do them.
First, turn your vessel, but leave it mounted on a waste block or in your chuck. Then assemble and make your handles.
Second, get some pressure sensitive sandpaper...the stuff with adhesive on the back. You can get rolls of it really cheap at Amazon. Cut some strips long enough to wrap around your vessel, or several pieces, if the vessel isn't a perfect cylinder, and attach them to where the handle will contact the vessel wall.
Third, attach the handle to a sturdy support of some kind...either a flat board, or a jig that can hold it steady. Then turn your lathe on slow speed, and hold the handle up to the spinning vessel. The sandpaper will (eventually) sand the handle ends to perfectly match the curvature of your vessel.
Finally, remove the sandpaper, and apply a dob of epoxy to the ends of the handle...not much, just a tiny amount...and attach the handles. I use 5 min epoxy, and need to hold the handles in place till it sets up.
While sorta crude, this technique has worked very well for me. The resulting joint is a perfect match, and the glue joint is stronger than the wood.