There are numerous tips in the FAQs to get better accuracy out of a Handi, they all apply to the superlight barrels as well, while the 243 is the most finicky of the 3 superlight barrels, they can be made to shoot very well as Stimpy and Howard NZ have shown, it may take a bit longer to find a load they like, but it can be done. If however you feel you have done all you can working with factory ammo, give H&R a call and they'll likely have you send it in, it could have a defect that is causing the poor groups.
I had mine at the range yesterday, shot a few different loads in it, the Remington 80gr PSP, and Stimpy's 100gr Speer handload shot the best, the Remington group below was shot within 2 minutes, probably closer to 1½ minutes, the other load was shot with 10 minutes between shots, bear in mind the ambient temp was over 91º at the range when the 100gr load was shot, so no a lot of cooling was happening!! All shooting was done at 100yds, grid on the targets are 1" squares.
Beside semi-floating the barrel which took about 15 minutes to do, I lapped the bore with flitz about 50 strokes on a patched jag, this was a new barrel that I just bought from holahead which I thank for the good deal!!
Tim