I decided to fight the land battle and charge right up the mouth of the American guns on the defended ford.
Surprisingly, I won. Lost a lot of men, though (almost 700). It was really close, and the AI might have won had it moved the hidden long rifle men who were hidden, guarding the other bridge. But they only came after I drove back the main force completely.
Also, at the end of the battle I had my general chasing the other general, who happened to run through a line of stakes set up earlier in the game. My general's cav lost five of seven horsemen as they tried to follow.
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