What I find interesting on the original post is that shinjin never mentioned slugging the barrel.
Shinjin, have you slugged your barrel? You can play around with different sized bullets, powders, and loads all day but if you want to find what works a little faster than doing that, you probably want to run a chunk of lead down the barrel and measure the bore groove diameter. From there, since it's an H&R, you'll have to concern yourself with the chamber size as Tim has suggested that a lot of the H&R's are over-bored and under-chambered. Definitely read the FAQ's on the 38-55. There is a LOT of good information there.
I can tell you this: I have an H&R and a Thompson Contender in this chambering and both are completely different in size. The T/C is a .375 and the Wesson and Harrington (H&R variant) is .3795. I use only cast bullets ranging from 245 to 265 grains in these barrels. I have chronographed some loads ranging from 1650 fps all the way up to 2000 fps with decent accuracy, depending on the powder type. Ironically, the Thompson Contender (with 8 inches of a shorter barrel) maintains better accuracy with heavier loads than the Wesson and Harrington. After a given velocity, the W&H groups tend to open up. That is NOT to say that the W&H is not accurate. It does a fine job at 100 yards with a marbles peep sight. I have fired groups at 1 inch with it.
What does all of this mean?? You're going to have to work with your rifle and find it's "sweet" point. If you wanna find that place faster, I'd recommend slugging the barrel.
Good luck. Once you get it working for you, it's probably going to be your favorite caliber to shoot and load.