Just a thought. If one were to experiment with solo playing ESR battles - historical or not - it seems the objective placement actually makes for an interesting prospect if you don’t look at the markers before placement. Only upon activation would you be aware of the exact intention of each force.
But I’m not convinced that fixed movement rates is good for solo play. I’m assuming here that the design choice for fixed rates was made for speed of play and simplicity (especially with multiple players).
So, one could I suppose roll 2 Davg +/- some modifiers for cavalry, ployed, and good roads, and roll for a formations regulating unit before moving it. Half moves would just use 1 Davg. This does require a rule for cavalry converting to attack directive either not closing the distance or reducing the range within the conversion can take place.
At least it would make it a bit unpredictable outguessing oneself.