The only way to tell for certain is to de-breech the barrel and measure the helix angle of the rifling at the breech and muzzle.
Anything else is just a guess.
The Log Cabin is a great place to do business with. They have repaired old guns of mine for about 40 years now. Still visit on Saturdays to shoot on their range.
Your rifle is a picket rifle, made to use a cloth patched bullet, likely about 1850. Remington Cast Steel barrels were the best in their day. Likely rifled with a gain twist and a choked bore. Nice old rifle!
The Leman rifle is likely one they made and sold through sporting goods and hardware stores, likely made around 1880.
The J.D. White rifle was likely made by a maker of that name in Carbondale IL. He worked from 1867-1890.
Hope this helps.
Your .40 caliber should not drop 10" at 50 yards with a .40 grain charge of fffg. It would drop that at 100 yards but not 50 yards. Are you sighting at 50 yards off hand or from a rest?
Sometimes the loading lever will, instead of releasing the ball after it is rammed over the powder, stick to the ball and pull it out a bit as the loading lever is pulled up. Relieving any sharp edges on the rammer or ensuring you use a soft lead ball will keep this from happening.