The .243 Superlights have long been the most problematic of all the Handi Rifles. If you have tried shooting it without a forearm on it and resting the frame on the front rest and it does not shoot, then there isn't much hope from it. Something about that set up just causes bad vibes. The .243 standard barrels can be troublesome too, but the Superlight is super iffy.
A friend has two standard .243 Handi's that he bought for his daughters. One shot reasonably well and the other would not group better than 5 inches no matter what we did to it. I hope this works out for you.
