Make a set of soft jaws for a vise using cold rolled steel. Close the jaws on piece of thin metal, 18g aluminum for instance. Tap your hole right down the center of the thin aluminum. Remove the aluminum. Don't lose the work offset you used for tapping.
Screw your part into the threaded hole and clamp the vise.
To make repeating the setup easier make a small reference hole in one jaw a known distance away from the tapped hole and use this to re-establish the work offset next time.