Perhaps to sort this problem out it is time for a bigger change. New troop types in even.
Light Horse: Parthian, Sassanid skirmishers, Greek and Numidian types who rarely, if ever, entered melee, unless against other true lights. Numidians would be superior here.
Light cavalry: Skythian, Hun, szekeler, Mongol, and Serbian Hussar types who could move around in swarms then concentrate for a decent charge
Medium Cavalry: earlier Romans/Greeks, Sassanids cavalry, early (pre-lance) barbarian types, Non-shock types who could skirmish but more often charged to contact when the odds looked reasonable
Heavy/Shock cavalry: Lancer types
The light horse could move as easily as LF and LH now, but get the same dice as LF.
Light cavalry move 6 MU and otherwise as Cav now but turn 180 for free (no armoured) and exceptional to be superior.
Medium Cavalry as cav now.
Shock Cav as shock now.
Basing would have to change
