For reference: This is the patent that I've found that makes the most sense:
Basically, the punch ram and the screw have ends that form opposite races for a ball bearing. The ram is retained with pin that goes all the way through the screw and a nut on top that allows the screw to rotate freely with respect to the ram (the ram in this case carries a punch, but the principle applies to a fly press).
This is all well and good, but I would have a really hard time machining a ball groove into these parts. If I can't find another solution, this is what I'll have to do. The mechanism I mentioned from my post drill doesn't provide for a lot of bearing surface - I'm afraid I would start bending or breaking parts which is dangerous when there's 20-30 tons involved.