If Jim were to start with a blank long enough to include the part plus a generous amount to chuck on he could eliminate the need for collets.
Clamp the blank in the 3 jar and do all the machining on the threaded end.
Part off leaving a little material for a finish cut.
Chuck on the threads. Use a split bush or pad the jaws with copper or aluminum.
Finish the big end.
If Jim is looking for an excuse to buy a collet setup, ignore what I wrote.
If using an ER collet be sure to make a plug to fit the back of the collet. With a short length in the collet it may be difficult to get the part to run true. Use a ball bearing mounted to a shank to push the outer end to run true and re tighten the collet. With a short length held in the collet it will be necessary to take very light cuts to prevent throwing the work out of the collet.