First you need to make sure you're shooting the Handi correctly, the Handi Basics 101 cover that, oil or solvent on the latch/shelf account for most Hand inaccuracy issues. You might try the 80gr rems, they shoot ok in mine, but it shoots 100gr Speer handloads much better, at least the first two shots. Other factory loads to try are the Federal Power Shok 100gr and Fusion 95gr, they both shoot good in my 243 bull barrel, see the best factory loads link in the FAQs.
Groups shot at 100yds.
Tim