Why would US sacrifice American blood for Taiwan when US won't even sell F-35s to the Taiwanese airforce like it does with true allies Korea/Japan?
It's because US is afraid of Taiwan Conquest by PLA will mean F-35's in Chinese military hands. US believes Taiwan is BEYOUND hopeless, that's why it refuses to sell the most advanced US weaponry F-35 that it sells to true allies.
You need to de-emphasize the "convincing" part because Westerners will always doubt China's side of the story. Taiwan can assassinate Xi Jinping with clear evidence, but US/West will always back Taiwan's side of story. There is no point of trying to persuade the West of what China is doing is good, they already think "CHINA BAD" .
A rational American leadership with healthy views of itself and China would likely not intervene, simply because the risks of nuclear exchange.
It is dangerous to assume that American leadership is rational. Trump for all his fault is not as warmongering as the neolib/neocon establishment, but if the US sees defending Taiwan as an opportunity to knock China out for good to defend its own credibility as the unipolar world power, it's hard to say.
You have a point about the negative perception of China in the US, however the flip side of that coin is that Americans are so ignorant on China and misunderstands China so deeply that they might believe it to be an easy victory. Most westerner's opinion on China is based on severely outdated information from the 1980s.
Even if China can win against Taiwan, it can still sustain crippling economic damage afterwards either due to sanctions or to coastal infrastructure being bombed. This is likely the main reason why the war hasn't happened yet, the process of winning the peace afterwards through maneuvering before the war starts isn't over yet. Development still comes first.
Therefore before launching the war, China will have to ensure its post-war economic safety by mastering key technologies, securing resources and establishing international systems that are not vulnerable to US dollar sanctions. It's all being done now, but those things are just as important as jets and missiles.
This is why Bismarck was so brilliant. He wanted a war with France to unify Germany, but he couldn't start it, and he maneuvered the release of the diplomatic conversation with the French ambassador in a way that will provoke France to declare war for him. He also made sure to secure future international relationships after declaring the German Empire, specifically having neutralized Austria as a factor before the war started.