So, after a lot of thought, I have found a solution - a "medieval force field" - or a way of representing the military limitations of the Lancastrian cavalry commander, at any rate. This manifests itself as a row of "impassable" squares running down the road on the Lancastrian half of the map. So, Lancastrian cavalry now can only cross to where their infantry are by the perilous route of the riverbank, or by going right back to their baseline and using the gap in the "impassable" terrain there. You can see how it looks in this first screenshot . . .
In this screenshot the play-test has reached Turn 9 (half-way) and you can see that just a couple of Lancastrian cavalry have made it across to the infantry. I think this is quite realistic . . .
Also, on Turn 9, the Lancastrian cavalry do have a chance to break through on the Yorkist left as they have "fragged" an enemy unit . . .

