What you need to do is bed and free float that rifle.

Its a relatively simple procedure if you are even a little bit handy.

You will need to remove the barreled action from the stock. Then you will need to remove wood from the barrel chanel until you can slide a dollar bill between the barrel and the stock all the way to the action. You can do that with a dremmel tool and sand paper easy enough.

Now this will most likely eliminate your issues. I would also pillar bed the action. Since your rifle is a LSS The laminated stock doesn't necessarily have to be bedded But I would do it anyway.

You should see significant improvements from the free floating. Of course there are many more things that you can do, but I think that free floating should bring your groups close to the magical MOA threshold.