Your wood lathe is the proper tool to turn something that slender. It
takes a very sharp chisel and a light touch to get the job done. A
steady rest on either lathe will help minimize the flexing.
Also consider setting up a trim router [$20 from HF] on the Atlas
toolholder. It will cut the wood with a lot less chatter. Better yet
make a dowelling jig for the router and turn small scraps into big
dollar value dowels that are very expensive to buy.
Bugs