I too have a handi-rifle in .243 and in the beginning the accuracy was very poor. Mine has the slotted aluminum scope mounting base attached to the barrel. This strip of course is aluminum and the barrel it is mounted to is steel. When the barrel heats up, heat is also transferred to the aluminum which has a higher rate of thermal expansion than steel and so the aluminum wants to get longer than the steel it is mounted to. The result is the aluminum will distort and depending on how your scope mounts are positioned on this strip the scope is going to be moved or distorted several moa. The fix. Cut this base into tow smaller sections so that the rear section is long enough to bridge the two back mounting holes. The small front section will only be held down by one screw. And the scope ring mounts should be located over the screws that fasten to the barrel. Now you no longer have a continuous strip of aluminum between the screw mounts on the barrel. Removing the center section allows the rings to stay in place over the screw mounts of the barrel and not be pushed out of place.
Another added approach I take is to only firmly or hard clamp the rear scope ring to the scope and only snug the forward scope cap enough to not allow the screws to come loose, but light enough to allow the scope body travel a little in the forward scope mount when it lengthens because it two is aluminum and if it heats due to outdoor temp or sun exposure the scope can lengthen without any distortion or twist. This is the only mod I made to the original aspects of the gun and it will should dimes at 100 yards all day without thermal effect and is not ammo sensitive. Hope this will help others too.