Do you have a scroll chuck?
If so, start by putting a blank between centers, rounding it off, and turning a spigot at one end. Then, mount the blank in a scroll chuck. Square off the face, and then cut a recess (1/16-1/18" deep). Using a skew, cut a dimple to locate the center. Then, drill a hole (5/16" more or less). Ideally, that would be done with a Jacobs chuck in the tailstock, but if you don't have a Jacobs chuck, you can use a 5/16" bit held in vice-grips. Finally, tap the hole using a 5/8x16" tap.
Now you have a threaded hole that you can use to mount the blank on the PSI threaded chuck (or on a 3/8" bolt held in your scroll chuck).