Set-screws with a 5/8 bore.
Actually, the cap-screw heads are for machine screws which tighten split cotter clamps tangentially to the bushings, not set screws which bear directly and radially on the bushings.
If you are not familiar with split cotters (clamps, not pins), they have great non-marring bearing on cylindrical objects, and are usually stronger than hell. However, they can take a little messing about to fit/make properly. In a nutshell, you've got a close-fitting bore for your cylindrical object (in this case a tool shank or bushing). Another, usually smaller, bore is made at right angles to the main bore, with about 1/4 to 1/3 diameter overlap of the secondary bore with the main bore. A chunk of stock, which becomes the split cotter clamp, is secured in the secondary bore, and the part that sticks out into the main bore is cut away. The cotter is then removed, cut in half at the midpoint of the curved notch (that's the "split"), the top part is clearance drilled and the bottom part is tap drilled and tapped for a machine screw. In use, the machine screw draws the top and bottom pieces of the clamp together, pinching the cylinder in the main bore with an exact profile fit. As the cotter itself is trapped in the perpendicular secondary bore, it's not going anywhere. (The machine screw does not intersect the main bore, so it's got to be located in the non-overlapping part of the secondary bore cross-section.)
On the Hardinge turrets, there's a nice convenience feature on the secondary bore and cotters. A small key (formed on my DSM-59 turret by a small inserted dowel) in the secondary bore engages a small notch running the length of the two cotter pieces. This keeps the curved notch on the two split cotter pieces aligned with the main bore even when there's nothing in the main bore. This is not essential to the clamp action, but a major aggravation saver when trying to insert a shank into the main bore.