A suggestion?... clamp the jaws shut or even a temporary tack and then run a drill down the centre to give vertical half round grooves, would help for holding a bit of round bar for end drilling, even better if you could do the same from 'end on' for helping to hold bar horizontally.
I`d put a lip or flange around the base so you can clamp it to the table of your drill press, so much easier and safer than trying to hold it if a larger drill bit bites your work piece