OP, I'd say for whatever reason the 147's and your rifle aren't working well together past a certain distance. Most reasons have been mentioned right here in this thread. BTW I've read quite a few posts of people having problems with 147's. Bet most of it is twist rate and/or worn throats, maybe even rifling profile, etc.
Having had great succeeds with 140 gr Berger hybrids I'd try those next. They worked great in my 6.5 Saum at a mile, even better at 1000Y, and that is out of a 8.5 twist.
I kinda went through the same thing a few months ago with another brand of bullet in my 6mmBR. That bullet shot okay at 300Y - like 3/4", and by 1000Y they were were absolutely horrible, like 3 foot vertical. The easy fix was 105 Berger hybrid which put in 4.5" vertical at 1025Y.
I am not associated with Berger bullets, they are expensive which I hate, but those are some awesome bullets for long range!!!