China could take over Taiwan in a month or less if they really wanted to though, so I wouldn't count on that being an obstacle if China and the USA get into a real war
They cant, because that is exactly what US is waiting for. A proper excuses to start the fight with China.
Or China can sign a treaty with USA for none-intervention during a "peaceful" partial take-over of Taiwan while letting USA to have the free trade she wants. (Or best, an integration with the Taiwanese governments on blockchain over governance of Taiwan.) I believe it is in everyone's interest not to have a full-fledge war in this day and age.
I am not entirely sure how it would be peaceful considering the state of Taiwan against China.