Could the new LAR-15M CAR A4 in .350 Legend from Rock River eclipse the 300 Blackout for hunting?...

The numbers say it should. With normal weight bullets for 30 Cal, your energy numbers put 300BLK behind the 30-30 and the 350LEG ahead of it. That's getting into hog range as well wherein people used to go with the 450s. For the AR10 and LAR platforms, I'd take a serious look at the 45 Raptor which is essentially a rimless 460 S&W. You can get the revolver cylinder modified to take the Raptor in moon clips and still use the standard ammo. I did have a 50A/E upper for the CAR. That certainly was a hog buster back in the day. But then the 460 came along....