Chainsaw Repair

You could always make long aluminum internal jaws for a three jaw chuck and use those inside a cylinder to cut the base.

Also for cutting pop up pistons you can make/purchase piston jaws that clamp on the inside of the ring land and use the ring land surface to square the piston up.

Either of these on a good quality 3 jaw chuck will achieve acceptable accuracy since you'll make the final cut on the clamping surface of the jaws on the lathe so they are matched to the run out of the chuck. Make sure to mark them so you always get them bolted back up in the correct position.