Taiwanese opposition leader Cheng Li-wun is preparing to visit the United States in June, aiming to leverage the political momentum from last month’s meeting with Communist Party leader Xi Jinping in Beijing.

Cheng, who heads the main opposition party Kuomintang, will also test her message on the Taiwan Strait in Washington.

In recent media interviews Cheng has outlined an agenda that goes beyond traditional party outreach, promoting what she calls “a new road map” for cross-strait stability –...