Yep, very few of us were there in 1874
The bluff in question is more like a flat topped butte or mesita with a little slope to the top. That distance was measured/surveyed later by an Army engineers unit and is recorded in the record.
If Dixon's rifle had a tang mounted sight it would have to have been the long range variety having at least 4 inches (400 +/- minutes) elevation. I think a barrel mounted "ladder" sight would have plenty of distance simply because of the sight geometry.
Doing the calculator thing assuminig an average barreled Sharps rifle zeroed at 100 yards shooting a 450 gr, 50 cal bullet with a BC of .3 with a muzzle vel of 1400 fps. The amount of additional rear tang sight elevation needed for 1550 yards is about 310 minutes or about 3.1 inches. (I tried it on my long-staffed Sharps and it will just make the additional 3.1 inches.) At the target, the bullet would be going about 600 fps and would take between 5-6 seconds to get there.
BTW there is a whole chapter devoted to this in MLV's excellent book, Shooting Buffalo Rifles of the Old West.