rickt,
My barral also has the typical H&R/Marlin 1:38 twist (if yours is 1:36, its actually a little faster than most, maybe that was a typo). Mine's also a little over-bored (0.431). I have had a devil of a time getting it to shoot light plinking loads accurately. It will shoot Winchester 240 JSP into a 3" group at 100 yard, which is fine for deer hunting, and why I bought this rifle. (FYI, the Winchester bullet measures .430", as do the highly regarded Hornady XTP and LE.) Light jacketed loads are much less accurate, presumably because they don't upset into the rifling. 210 grain .431" SWCGC cast bullets from Montana bullet works (loaded over 7 gr Unique) do give me good performance (1.5" groups at 50 yards). But those bullets are fairly expensive for everyday plinking. The Lasercast are half the cost, but also half the accuracy (and more likely to lead the barrel). In my gun, 200 grain .429" plated bullets perform similar to the Lasercast IF loaded heavy enough to upset into the rifling, and are more expensive. The slow rifling in the 44 has a hard time stabilizing slow heavy bullets, and is one reason I've been thinking about switching to 357max, but I haven't done so yet. Primarily because I've been so happy with the terminal performance of the 44 on deer. (Again, the main reason I own this gun. And I've now got a nice 223 barrel for this rifle which is satisfying my need for accuracy.) Anyhow, in my experience, the best route to accurate plinker loads in H&R's 44 is to use large-diameter bullets that will fill the rifling without obturating, and that are light enough to stabilize at relativlely low RPM. The .433" round balls seemingly fit that criteria very nicely, and are probably worth a try.
Duane