The secret to making threaded back plates is to make a replica of your spindle nose to use as a gauge. Make this piece to the highest level of accuracy that you can and over the years you will use it many times to make an adapter of some kind to fit your spindle.
You bore and thread the spindle from the back side so that you can turn the recess, face the mounting surface and single point the threads without taking it out of the chuck. If you have made your gauge carefully, you will be able to screw the new backplate onto the spindle and then fit the front of the backplate to the chuck. When you have the chuck mounted to the backplate, put adjacent punchmarks on the chuck and backplate so that it can be removed and replaced in the same position. HTH Stan