We played this again and the British managed a victory rather similar to the actual one. My report will be delayed by Real Life, perhaps until later today or more likely tomorrow.
Edit: also, the cavalry was able to respond quickly to a threat on the opposite flank. Their brigadier made no fuss about giving up his cavalry regiment. But then almost all rules, even more complex ones, would allow this. I want simple rules that avoid hangovers from too many calculations.
In the actual battle, the British were rested and had not yet begun to suffer from malaria. (They were camped near swampy terrain.) The French had made long forced-marches through the intense heat of a South Italian summer, the battle being fought on July 4th. I still might tweak the scenario before posting it.