Hi Miles
if you are worried about it, cut the piece of mdf you have roughly to the shape of the top, glue it to the top, when dry mount in the chuck, then you can bring your tailstock up for extra support, turn your outside to the shape you want, then part through the middle of the mdf and turn off the band of mdf, or use a disc of timber the same way and it will give you a contrasting rim
cheers
Andy