I think your muzzle velocity is up to 50% low. This page shows some modern .50 cal muzzle velocities. I think the old ones could probably do about as well. Their ignition was not nearly so energetic, but they had longer barrels and could likely burn more of a larger powder. I charge. A .50 cal lead ball weighs about 187 grains. With various powder loadings they show muzzle velocities of 1331 to 1863 fps.
But I found some info on something more like they might have had in 1775-81.
They had .54 caliber rifles. Using a BC of .075, for a .54 caliber, 237 grn ball, a 2000 fps muzzle velocity and usingRenegade Rifle Ballistics calculator, it is do-able, but you get one heck of a rainbow trajectory. The highpoint, at about 300 yards is about 160 inches above the horizontal. You'd have to know the range very well. But lowering the taget range to 400 yards reduces the height of that rainbow by half to just over 80 inches.
I got the muzzle velocity and the BC The Complete Blackpowder Handbook
So, I concede that 500 yards is a bit much, but 300-400 probably happened. (300 yards reduces the height of the rainbow to about 36 inches) At 300 yards, nominal, your range estimate could be off by as much as 15 to 20 yards, and you'd still be within +/- 10 inches, not taking into account all the other variables.
But at least I found an interesting toy to play with.
intersting. those muzzle velocities are amazing. surprised that the metalurgy of the day would support that much pressure.
speaking of rainbows, i had a barrett 50cal for a bit. sighted at 2000m. i dont remember the ballistics exactly but i want to say the drop was like 14 feet or something. now thats a rainbow. course when it arrived it definately had something to say.
still could punch hole in 1 in steel plate.