I'm not familiar with that rifle and only a bit with Henry's at all. They seemed well made and well finished.. Almost any trigger can be helped by judicious smithing. Use stones to polish friction surfaces in the trigger linkage and the sear surfaces...just polish. They don't need to be mirror polished just remove the feel of roughness..usually just the worst of the machine marks. This is usually done with Arkansas stones (shaped) or ceramics. I prefer the ceramic stones as they cut a bit more freely and lubricate with water, or they can be used dry. Dry causes more problems when the stones need cleaning but not too bad. You can also use wet-or-dry silicon carbide paper but keep it flat and backed with something, and lube it with water.. Start with 600 grit and go up if needed. The flexible nature of the paper (cloth) material makes its' use a bit more difficult nut it is cheaper, I've used it in the past and still do for large flat surfaces.. Dimenions are very critical as are the angles that form the sears.. If those angles are changed the weapon may become fangerous. I usually also polish the spring contact surfaces as well as the hammer surface that the bolt contacts to cock the rifle. I always debur the receiver but seldom polish the insides unless there is an obvious and agregious problem..
