I think I'd make the end pieces on the lathe, like boxes, and the handle separately, then I'd chase the threads on the boxes, and have two boxes and one handle. I'd get out my coping saw and make the three pieces into one piece, with a lot of hand carving and sanding.
I'd make sure that the boxes and the handle had lots of thickness to them so I could shape and sand the piece into one unit.
I also think you are going to make more money flipping hamburgers than making this telephone, per hour
The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
William Arthur Ward