Ive only had my lathe for a while so im no ways near an expert,but i would try 2 things.
1--switch to a 3 jaw chuck and use inside jaws and clean up as best as possible.
2--go to a muffler shop,harbour freight,somwhere that sells cheap tools and get a tailpipe expander.Its a tool that looks like a mandrel with slices all around it and when hammered into a muffler tailpipe or thin walled pipe it makes it round again.This might work if a bolt could be installed through the middle and then the cylinder put on it and tightened down from the end with a washer to hold it snug.Then run it in lathe and clean up as best as posible.
If all fails,get another cylinder and make a better mandrel.What echo is that cylinder off of.