To the original poster:
Back in the day that those 2000 yard (or 1600 or whatever) sights were designed, the infantry theory was point and area targets. A point target would be hitting something very specific (generally, a man... but maybe a head) whereas an area target was just that, a large area. Think of the space a company of the 19th century would occupy. A hundred men would march in something like ten files by ten ranks (or, maybe a 12 x 8 or three 4 x 8's or 10's with a gap) A 10 x 10 company falls in to about a 30 foot x 30 foot square. You're aiming for the "blob" any hit on anyone anywhere in the blob is the goal on those 1000 ish to 2000 ish area targets.
Ranging practice in the latter 1800's in the US Army was a part of the soldiers "qual test". You not only had to shoot a certain score on the known distance range, but you spent a day doing ranging exercises (or passing ranging tests) that were based on two styles. In one, a line of troops marched away from the "testee". He had to direct one troop to 'drop out' at each 100 yards from 100 to 1000 yards. To pass this, the soldier who stopped had to be at X yards +- y yards, according to standards. The standards for "Expert" were quite tight, like +- 10 yards at 500yards. You acquired these skills by frequent practice and drill. The other style of the test was just being quizzed on random objects, such as, "soldier, range to tree this side of bend in brook". Col Townsend Whelen talks about these tests in his books, such as "The American Rifle" and "Suggestions to Military Rifleman".
In the time period of the Civil War and Indian wars, the army use to issue a piece of brass (about 5 inches by 2 inches ) with a slot in it. The slot was tapered. You would frame a standing man in the slot, and read the distance on the scale.
A range estimation method that used to be taught in the army used the lensatic compass. It is a trig method. The 5 degree rule. Take a bearing on your 'target' move perpendicular off your sight line, counting your paces. Continue to take bearings till you are 5 degrees off your original bearing. Your original target distance is 11 1/2 times your pace count to your 5 deg offset.