Finish turning the center first before thinning the ends. Reduce your tailstock pressure to the minimum needed, too much and you will bow the piece. Or hold one end in a chuck and only use the centering pin on your tailstock-- little or no pressure. Gentle cuts with a sharp tool, push too hard and you will bow it. Support the cut with fingers on the back side when working towards the middle. Once the chatter starts change the speed of your lathe-- faster or slower-- to get away from the resonance frequency and take very light cuts. Try a skew rather than a gouge, most spindle turning cuts, deep coves excepted, are easier and cleaner with a wicked sharp skew. All else fails get out the 80 grit gouge. ;-)