Think your missing the point.
Plant a variety which has milling genetics such as Solstice and it will naturally have higher protein than Santiago.
Even if you only achieved an 11.5 protein today's that's worth nearly about £15/t over the feed price.
Not all soils will grow high protein wheat, regardless of variety. Growing a milling wheat on chalk is going to need 300 kg/ha of N to have any chance of making the grade. An extra tonne/ha of a feed wheat exceeds chasing a premium that I'm only going to make 1 year in 2. I put my resources into growing low protein spring malting barley instead whcih I can do cheaply year after year.