Hi buddy,
I when I was breaking in the SS TD barrel I was cleaning it right in the field each 2-3 shots using copper brush, jag and Rem "Brite Bore" spray can.
Then 2nd outing I was using just a bore snake, did 2-3 passes after switching ammo.
After this I did more thorough bore cleaning at home using jag and Hoppe's copper removal liquid. I didn't shoot it since then yet. It is damn rainy weather here in Canada this week. I removed the barrel band and waiting for another chance to go to the range...
I don't have a chronograph.
Did you follow the torque specs for your scope rings? Or just by hand feeling?.. I had a similar problem which was solved by using a proper torque wrench (Wheeler Fat Wrench) to apply correct torque values. No problems so far. Also, I use Burris Zee scope rings with eсcentriс +/-10 MOA polimer inserts -- these enable you to boresight the scope before tightening it up. No lapping needed, no scratches on the scope. You set each turrent in the middle (normally for a new scope it is already done by factory) then manipulate/rotate only those plastic inserts to boresight your scope. I love this idea. Intstaled the same kind of scope rings on my BLR too.
Here is the ammo list. You've made me to look up the invoice.

Disregard the prices - those are in Canadian dollars ))
Federal Extremely Low Drag 308 Win 178 Gr eXpanding ELD-X Box of 20 × 1 $53.99
FEDERAL VITAL-SHOK 308 WIN 150 GR NOSLER PARTITION BOX OF 20 × 1 $54.99
Federal Premium Berger Hybrid 308 Win 168 gr Berger Hybrid Box of 20 × 1 $52.19
Sako Gamehead 308 Win 180 Gr SP Box of 20 × 2 $85.98
Sellier & Bellot 308 Win 150Gr SPCE Ammunition Box of 20 × 1 $35.99
Sellier & Bellot 308 Win 180Gr SP Box of 20 × 1 $35.99
Federal Power-Shok 308 Win 150Gr JSP Box of 20 × 1 $32.99
-- the Federal Power-Shock and Sako have shown best groups so far.
p.s. My other rifle (Sauer 100 XT 6.5 Creed) loves Sako ammo too. Also, Hornady ELD ammo groups well out of Sauer barrel too. I was able to make 3-4 shot touching holes groups at 250 yds - which is less than 0.5 MOA