Welcome! Try some heavier bullets, H&R 243s seem to prefer lighter or heavier bullets, no rhyme or reason, but most find if theirs won't shoot one, it will the other. I Have 3 of em, 2 shoot 95-100gr good, but don't like the 80gr that the other one shoots good. I'd recommend the 95gr Fusion or 100gr Power Shoks, both by Federal. If you want to try another lighter bullet, the 80gr Remingtons or the 55gr Win Supreme Ballistic Silvertips, all of these have a good reputation in 243 H&Rs. Be sure to read the Handi Basics 101 and the accurizing help in the FAQs, there have been many down the path ahead of you, take advantage of their help.
Tim