Instead of doing a lot of cuts with a long rod, I'd start by making about-the-right-length
cylinders (maybe just with a hacksaw), and holding them in a collet
or (even better) soft jaws in a 3-jaw chuck. Finish one end square, so that
when you reverse it in the soft jaws, the soft jaws can act as the stop for a
second operation that makes the 3/8" nub and cuts to length.

The result would be a batch of parts, going from a rod, to rough cylinders,
to one-end-flat cylinders, to one-end-flat/one-end-stepped finished
length parts.