To really get the most from your original Trapdoor, consider reloading for it.
1. The military 3 groove barrels in them normally require a cast bullet sized to .460" or so for best accuracy.
2. Frankford Arsenal infantry loads were originally loaded with a 405 grain bullet at 1,300fps. Later rounds for the 1884 and 1888 models were loaded with a 500 grain bullet at 1,300fps.
3. Cavalry loads started and ended with a 405 grain bullet at 1,100fps.
4. If loading with black powder, use a very soft lube like SPG or a mixture of beeswax mixed with Vaseline.
I load most of my fun loads (i.e. cowboy type loads) to 1,100fps with the Lee or Lyman 405 grain bullets cast fairly soft (20 to 1 alloy) and enjoy fine accuracy. For long range shooting I up the velocity to 1,300 fps.
Have fun with that old Trapdoor. They are amazingly accurate at long range. 1,000 yards is child's play with them when using the infantry load.
One final note: Trapdoors with the original front sight shoot high (6 MOA or so) with smokeless powder. You'll see many of them with a taller front sight to compensate for the difference between black powder and smokeless loads.