Hi,
I would propose to give units 2 different movement traits, one gouverning tactical movement speed (in a battle) and one gouverning strategic movement speed (on the map). The reasoning is that how quick you are in a battle situation does not have a whole lot to do with how quick you can cross long distances on a forced march situation. Golems for example arent very fast, but also dont tire so they could move quickly strategically but slowly on the tactical field.
One can also add a "forced march" trait that makes infantry be able to keep up with horse troops on the strategic map.