6mm fatrat would be my choice with no recoil 100-200 yards.
Anything over that would be 6 cm or dasher.
I ran a 6mmAR Turbo40 out of a gas gun for my first year in PRS (pretty much the same thing as a 6mmFatRat). It did pretty well even at the 1000+ yard distances. Pushed hard out of bolt rifle, I don't think it would give up much to a 6-Dasher. Didn't mention it because OP said .473 bolt face.