I still think archers need some way of evaluating their success, thus line of sight. An archer is a man, not a machine able to train in by varying a few degrees elevation, or traverse...
Also enemy troops tend to move, especially under fire, and someone barking stuff like: " you overshot, you incompetent milkdrinkers", or " archer block, WHEEL left, 1, 2, 3 Halt...Take aim!... Loose" is not going to produce more hits... I think that its much more productive; when shooting from a higher vantage point, looking over your troops, and choose another target when the current target is engaged in melee.
As with the lancer/ archer mix... Aren't those the units of Noblemen of Byzantium, known for their cowardice and ineffective fighting? Wikipedia gives me that all cavalry units, except the cataphracts, carried composite bows, but also states that they were only used against light troops, probably due to the ineffectiveness against heavier armor types.
Anyways: most of your facts check out, but I saw opportunity to make a few side notes...