I have the same set up. Savage 110 Fcp in .338 lapua I changed my stock to a manners t5 and have a vortex viper pst
ffp 6-24x50 on it as well. My gun wouldn't shoot the bergers at all. The SMK's are what it likes combined with 92.0 grains of h1000 and it is a deadl combo.
I have been thinking about swapping sticks as well but with a blank costing 350 ish and another 250-300 in gunsmith work it is a hair pricey for a gun that already shoots. I was thinking 30-32" bartlein 1-9.3 twist.
Keep me posted if you swap barrels. Would like to hear what that barrel will do for you.