I haven't personally owned on of the ER Shaw rifles, but I have had a few Shaw barrels. They were both good shooting barrels. I wouldn't call them target barrels, but both shot under 1" groups with everything I ran through them. Both were capable of .75" groups with the right load.
The action used is a standard Savage Action and I'm a big fan of those. My only thought would be the caliber. I love the 375 H&H, but have you considered the 375 Ruger? The Ruger is a better match to the Savage action and will be a little cheaper to shoot (brass and factory ammo).
All I can say is that you should get the spiral fluting. I love the looks of it!
Andrew