JacobChuck makes all sorts of mounts.I will look into the Jacobs chuck. Is this chuck press fitted or held on with a screw. The chuck on this machine press fitted.
The popular "press fit mount" is known as JT33 (Jacob's Taper #33)
You may also need to determine whether you Arbor shaft and bearings are OK and true first because JacobsChuck may solve say only 75% of your problem.
Use a dial gauge to test how true is the shaft when spinning.