Instead of strategic ambiguity, I have a much more elegant solution to the problem of Taiwan: If China invades or peacefully reincorporates Taiwan, we should nuke...Taiwan. First, that destroys Taiwan's incentive to start provoking China once it receives a US security guarantee, it also encourages Taiwan to spend on its own military since it would see invasion by China as an existential threat (in fact, it gives it more reason to invest than if we simply withdrew our protection), and it eliminates China's incentive to invade---as the territory itself and the troops occupying it would be incinerated (and the radiation would make the island uninhabitable). However, it also doesn't make sense to retaliate with a full-scale nuclear onslaught because someone nuked a territory that was not, de facto, yours yet either. It places China in a weird place game theoretically. We can threaten this action much more plausibly than we can a full-scale attack on the Chinese mainland, it will make Taiwan behave itself, and China would not respond to it with a full-scale nuclear assault because, well, after it they are essentially in the same position they were before the invasion. From their perspective, it would be like nuking the US out of the blue.
I know it is terribly immoral, and incredibly dishonorable and monstrous and all that jazz, but there is a certain beauty to it: King Solomon himself would be impressed.
If everyone behaves rationally, it is far and away the most effective means by which you could defend the island. Of course, that is a big if—a very big if.
This isn't a credible commitment (the only president in US history who might have been believed if he announced this policy was Nixon, and then only in 1971 right before going to China), so while on paper it's elegant it will fail IRL.
The better course of action is to research a cost-effective guided missile that can blow up a landing craft at a range of ~20 km, then build 100,000 of them and give them to Taiwan. Amphibious assaults are hard, and the CCP is almost certainly unwilling to endure the losses necessary to take Taiwan if Taiwan were capable of sinking high thousands of landing craft.