I wonder if that wouldn't be more stable/secure if rather than just the end of the screw bearing on the work, a shoe of sorts, similar to a moving vise jaw or c-clamp jaw to be attached to the screw in an analogous way. Essentially just making one whole jaw of the three jaw in two parts with a adjusting screw in the middle making the whole jaw longer as needed.

probably a lot more hassle and trouble than just doing it a 4 jaw like it is supposed to be :-)