What would be the most effective strategy?

The way that the Rebels did it. Use guerrilla tactics; harry their supply lines; ambush patrols; etc.

Fight on the other side of an ocean from their normal supply lines. Attract a rival European power to threaten their naval superiority and supply ships. Bankrupt them.

Wear clothes that blend in to the countryside, don’t allow fighting in formation. Hide behind trees and rocks and take shots at them. Strike by sneaking up to them and shooting, then retreat into the swamp.

Put the kettle on.

Don’ forget to shoot the officers first.

Don’t shoot until you see the whites of their eyes.

Surrender immediately and accept The Crown as your rightful and legitimate sovereign.