I have a 7x57 #1 International (aka "RSI") with a light 20" barrel and
if I allow the barrel to cool down until it is just very slightly "warm", it shoots very small 3-shot groups... the smallest being just .179 inches at 50 yards... and it
averages 3-shot groups of
less than a half-inch at 50 yards with the best "accuracy load" (the best one I've found so far) of 47.6 grains of H4350.
My #1 "loves" H4350 and with a maximum load of it (50.0 grains), I get about 2785 fps (haven't chronographed that "hunting load" yet) and have shot 3-shot groups of .404 inches at 50 yards with that load.
Factory loads for 7x57 (aka "7mm Mauser" or ".275 Rigby") are vastly UNDER-POWERED... and to get any real performance out of a 7x57, you really should be reloading your own ammo. If handloaded to 50,000 CUP (a max load using 50.0 grains of H4350), the 7x57 Mauser out-performs the maximum loads in a 7mm-08 (averaging about 53,000 CUP) by a slight margin.
It sounds as if you're having the same trouble I have with my Mannlicher-stocked RSI... the thin barrel is heating up and touching the stock's wood thus changing the barrel's natural vibration as the bullet travels down and out the barrel.
Since any game you shoot a bullet at will be fired from a
COLD barrel (the first shot or two, anyway)... I suggest you just be patient and give the rifle's barrel a little time to cool down between shots from the bench-rest since the coolish barrel is pretty representative of where the rifle will shoot from a "cold" barrel under hunting conditions.
I realize I could spend a lot of money, time and frustration on my little RSI, but in the final analysis, it wouldn't be any more accurate on the first shot or two than it is now... and so I've decided to just be patient.
To that end, I bought a little CZ453 "varmint" model (w/heavy barrel & no sights) with a factory-installed single set trigger to "match" the Kepplinger Single Set Trigger I had my gunsmith install in my RSI. And I simply shoot 3-5 five shot groups with the CZ between EACH ahot from the RSI... and things work out quite well since both rifles have duplicate 4-12x40mm A/O scopes on them and both rifles have single set triggers to aid in the simplicity of going back-and-forth between the two rifles when I go to the rifle range.
Normally, my goal is to shoot the smallest possible group while keeping ALL shots within the diameter of a bright orange target paster. So far, this has worked out quite well.
Jus' my 2� worth...
Strength & Honor...
Ron T.