My grandfather gave me an old craftsman lathe years ago. It had a motor that was separate from the lathe and mounted behind the lathe to attach the pulley to. It did not have a bed like most lathes now have, it had poles that the tail stock slid on. I lost the live center while moving and had the same problems you are having finding a new one. I upgraded to a harbor freight mini and then to a Delta Midi, but as far as i remember, the live center was straight shaft or almost straight. It did not seem to have the taper like the ones I use now. It was about two inches long or so with a point on it. With mine, I had to use oil where the live center spun in the tail stock. I don't know if you could have one made at a machine shop or not. I wish I knew where mine was, I would be happy to send it to you, since that lathe hasn't been used in probably 10 years or so. Good luck.