Yorktown mission of Nathaniel campaign in hardest level

I'm struggling at Yorktown, the last mission of "Fire" campaign. I started the game normally and build up my army and some culverins to snipe the first few cannons in the British base. However afterward all my army will be overwhelmed by the horde of British and German armies, which seem to be spawned instead of created. Eventually I run out of resources in the south and I can't afford more culverins to snipe down the rest of the cannons, while the Brits and Germans seem to get stronger. And Lafayette is just a completely useless ally like most allies in AoE2 and AoE3 campaigns.

Does anyone have good tips for this mission?