I don't think it is a cornish. White leghorn or a mix of it. Or white rock like you think. I don't know what that hatchery sells.
My daughter says the comb is a pea comb and rose comb cross.
I am concerned about the black spots on the comb. I went to a workshop last month and there was a chicken disease that had black spots on the comb. Might want to do some research.