Popapi, I would love to use that 165 Matrix. From the test results I have read, it has a true BC almost identical to the .337 G7 BC of the 180 gr 7mm Berger VLD's I am shooting in my LR 7 rem mag, and those are some very good bullets.
I spoke with the guys at Matrix and they told me my 10 twist barrel would not stabilize the 165's, or I would already be using them.
I would also ask, why do you want to use unleaded bullets? By time you reach 500 yards your speed is going to be much lower anyway, so how is that bullet going to expand then?
In all fairness I have used the Barnes TSX bullets in both a 270 Win, and a 300 WSM
. They worked quite well, but ranges were only 300 yards, or less. IMO, they are not the best choice in a longer range bullet. You need BC man!