As has been said, the Superlight 243 barrel is troublesome, even the standard contour 243 is a consistent good shooter, there's considerably more material in any standard contour H&R barrel, they're often described as bull barrels since they're on the heavy side compared to other sporter barrels, but the 22" and 24" bull barrels are the best choice if you want consistent accuracy, specially with a warm barrel.
As for getting the Superlight to shoot, if it was shooting good for you at one time, I'd be looking at the Handi Basics, in particular making sure the latch and shelf are dry, that alone is the number one reason for inaccuracy reported by H&R gunsmiths, and the easiest to fix. The next thing I'd check is how well the barrel fits, if it's lose when the action is closed without the forend on, it needs to go back to H&R for a replacement barrel, the underlug on high pressure chamberings have been known to setback causing the barrel to be lose on the frame when locked up.
Tim
