What exactly do we control? How do you relinquish something you haven't got?
Control of the strait is not exactly a navy vs navy issue... the US Navy's problem in that area is proximity to the mainland and land-based missiles and aircraft. For that reason, the US response to an imminent invasion - it's not like the preparations could be kept secret - would likely involve interdiction on inbound shipping (oil and other raw materials) and outbound shipping (manufactured goods bound for Europe, Africa, and the Middle East) in the Indian Ocean.
I personally think such an invasion is so unlikely that discussing it is largely a hypothetical exercise... look at China's minimal military sealift capacity. Do you think anyone would seriously want to mount an amphibious invasion on the scale of the Normandy landings in the age of satellite surveillance and guided missiles?
If the Chinese economy crashes (a real possibility), leading to major turmoil and the rise of a militarist government, then it's a possibility. Other than that, not likely.
What economic leverage would that be? Economic leverage is a major factor deterring such an invasion.
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