Hello,
This sort of problem can lead to a maze of discussion possibilities.
I suggest that you remove the woodwork from the action, (Making sure that the little steel tube - if there is one - which lines the REAR action screw through the woodwork, does not slip sneakily onto the floor and disappear unnoticed),
Then have a look at the barrel channel in the woodwork.
If enough shots have gone up in the past, and the woodwork has a tendency to warp when it gets damp or during atmospheric humidity changes, you will see metal-contact discolouration or a shiny area where there is contact.
(I'm taking about a free-floating barrel here).
This is most often from right or left. Contact destroys the ability of the barrel to whip naturally and thus changes the point of strike.
Dependent upon how the action is bedded, a heating barrel might be moved to contact the woodwork, but in my opinion a medium hunting barrel should bear half a dozen shots without a problem.
I used a cheap old PH Safari .243 with Norma ammo for 18 years before the barrel wore out. It knocked over up to a dozen hinds at a go and retained it's accuracy. (I had taken it apart and re-built it, customising the trigger, stock and 'scope mounting).
Different makes of ammo can create totaly different vibration signatures along the barrel - thus the heavier barrels pay dividends as they are more stable to start with and are often more tolerant of various bullet weights, delivering them to point of aim.
The old-fashioned game rifles - such as Rigby - mostly had forends as short as a shotgun. The woodwork was hard onto the barrel but as the wood was from an era where there was more timber and better chances of proper seasoning, the shortness and stability of such stocks meant that there was less likelihood of stock movement - AND they were often carelessly soaked in gun oil which helped prevent moisture changes.
Modern stocks are often not so obliging, and some of those are so flimsy that they warp under hand pressure. I have fired some lovely looking rifles and felt the forend twist under a firm shooting hold.
(There's also the occasion fall from grace when the forend handhold changes by accident to include thumb pressure on the barrel).
So, in some cases we have a free-floating barrel which warps for various reasons - sometimes staying against the barrel on one side - and which will again move once that pressure is removed.
On the other hand we have a barrel-contact forend - often done with one or two steps machined into the barrel channel upon which the barrel rests when the action screws are tightened home.
That's fine if the wood is stable - but if it's not, then you get varying prressures against the barrel from the woodwork dependent upon the weather.
So, in this age, you are probably better with a free-floating barrel - and even the synthetic ones are made free floating.
OK. Sort yourself out with a clean working area and a vise or carpenter's workmate, padded with cardboard and/or rags.
Fix the stock in there - firmly but not crushingly, and obtain a rod which will fit loosely in the barrel channel.
Round file - piece of dowelling - metal tube. It doesn't matter.
Now get your sandpaper and roll it evenly round the rod so that it sits easily into the channel and with even - straight pressure strokes file away the wood to be removed - checking the fit of the barrel and action regularly.
DO NOT intrude your wood removal device into the action area.
Patience is the watchword. An hour in the workshop will give you so many hours of pleasure and feelings of security in the woodlands.
If you achieve a nice even fit of equal spacing around the barrel - check with a thickness of paper slid down and easily moved after the stock is fitted, and if the wood moves again in a week or so, then repeat the process.
If the stock insists on moving all the time - then another stock is required. (Very rarely this happens).
Treat the barrel channel with a generous application of vaseline, the re-assemble - re,memebering to replace that little rear screw tube which acts as a pressure spacer in the woodwork.
Turn the front action screw - with a well-fitting screwdriver - as tightly as you sensibly can.
Turn the rear action screw back in medium firm. Not wrenched up but tight enough not to turn itself out again.
On the ammo side of things. Every ammo manufacturer seems to have their weak points and every rife has its tolerances.
Now think of precision in assembly if you don't 'roll your own' and try RWS, Norma or Sako.
In the calibres I've had dealings-with, I must admit that RWS was always an excellent test-base ammo to see if the firearm was behaving Ok to start with.
Faster and lighter is not always best, even if it is the on-going fashion. A .243 barrel whilch likes lighter bullets might not necessarily stabilise the 100 grainers.
'Depends on the rifling twist. Give RWS soft point - semi pointed a try and see. If you only fire a couple of boxes or so per year - then it's only a few pints of beer.
The paramount item to remember, (hoots and derisive calls from some parts of the gallery, but rememeber that variius deer agencies will be browsing these sites and looking to see if they can add ammo to their cause of even more policing and tests), and it supercedes all other considerations, is that at some stage the hunter intends to have an innocent living creature in the reticule of that 'scope. It deserves a clean end and not hours or days of misery.
Bear in mind that your conscience also has to deal with it. I've created a blunder or two in my years which caused me sleepless nights, and I've had to learn to live with it, but not easily.
Believe me, several single animals lost and wounded out of more than several thousand successes are VERY easily embedded on your mind.