I finally found a load that works in my Saiga 223.
Hornady 55gr FMJBT bullets, LC Brass, Winchester primers, 23.0 gr IMR3031.
Shot at 100 yards, 1.5 inch groups. Some would call the group sizes 1.5x1 (1.5 high by 1 inch wide) Used a red dot sight that covered the target. I could probably cut those groups in half using a scope with cross hairs. Saigas can be accurate, but only if you work at it. Beats the heck out of that cheap steel cased stuff that I have been shooting.
I might back down to 22.5gr of powder because by looking at the primer, I'm right on the edge of over pressure. Other than that, I am very pleased.