I have a Savage LRH. 24" barrel. First thing you should do is make sure the barrel is fully floated and making no contact with the stock. If so, clear it with sandpaper/dowel and torque the stock bolts per the instruction manual. Both loads produce .25-.5 MOA consistently, and tested out to 500 yards in my rifle:
Lapua Brass
Redding FL S Bushing Dye, Redding Competition seater. Neck bushing size .292"
Berger 140 Hunting VLD's. Seated .075" off the lands.
Load 1: H4831SC 53 grains , Fed Match Primer. 2940 FPS, ES 10-15FPS
Load 2: Retumbo, 59 grains, Fed Magnum Primer. 3015 FPS. ES-10-15FPS
Note: bullet seating depth does make a difference in pressure and accuracy with these bullets. I saw a clear accuracy improvement seating .075" off the lands, Lower pressures, and lower ES. I also have a Cooper that shows the same effect with these bullets. If you seat close to the lands with these loads, you could see pressure signs. Work up with a couple of grains lower with both loads. I have seen lot variations of +60 FPS with Retumbo. Recent lots are hotter than the older lots of two years ago. This load is with the recent lots.