Your dilemma has a simple solution. It's all about the timing. An underlying assumption of your dilemma is that the fighting on Taiwan will take a long time, during which the US can prepare and then intervene. However, if the conflict is decided in a week or two after which the PLA controls the strategic points on Taiwan, then the US can't stop AR anymore, they'd have to take back the island. Defending Taiwan against an American counteroffensive will be a lot easier
If we assume it takes about a month for the US to surge assets in bases surrounding China, then China just needs to prepare to take over most of Taiwan within 1-2 weeks and keep enough buffer for preparing defences. Then the Americans will have a dilemma: do nothing and look weak, leading to lost international influence or try to take back Taiwan from a very unfavourable starting point
So if China is prepared for a very fast campaign on Taiwan, then the US will be forced to intervene early to make a difference, at which point they haven't brought over enough assets to pose a danger. China can survive a few bombs coming from the aircraft currently on Okinawa and then strike all American assets in the Pacific.
The real danger is the return of large numbers of US troops to Taiwan and a fortification of American bases in preparation for a US supportes declaration of independence
There are two reasons why I have not considered this as a viable solution.
1: The ability of the PLA to conduct AR in a relatively short time span (1-2 weeks) is one that I am not confident the PLA are able to do yet in the near future. It's not out of the question for them to develop the forces for, but I do not yet think they are there. Notably, the shorter the timespan in which they seek to carry out successful AR means that they'll have to contend with a military force on Taiwan that still likely has some reserves of fuel, food, water remaining, as opposed to if they spent a month doing comprehensive bombardment before initiating landings.
2: The bigger issue is that even if hypothetically the PLA completes AR within 1-2 weeks and let's say it all goes well and swimmingly, there is no guarantee the US will simply accept it lying down. The US does not necessarily have to "take back" and "reoccupy" Taiwan, but they can still exert significant military force to meaningfully degrade PLA capability even after AR is "completed". For example, the US can aim to substantially degrade and target PLA air and naval capabilities in the eastern theater command (or even westpac region overall), and to target Chinese shipping/resupply efforts between the mainland and Taiwain island. The goal of such a campaign obviously would not be done for the health and wellbeing of the civilians on Taiwan any longer, but rather as a punitive way to degrade PLA capabilities to try and force China to accept terms of peace that are less favourable than China would prefer.
.... of course, both of those reasons 1 and 2, can still be mitigated by a "simple solution" --- which is to say, having a much more capable PLA.
If the PLA were capable of successfully prosecuting AR in a very short timespan with very short warning, and/or, if the PLA were also capable of fighting and credibly winning (i.e.: not a pyrrhic victory) in large scale westpac conflict against the US even if the US were able to have some time to surge/reinforce its westpac position, then yes that would be a solution indeed.
What you are suggesting in terms of the US massed forward deploying forces in Asia is little different from the Ukrainians stuffing their trenches, which are in artillery range of many many Russian guns, to the gills with more men and equipment.
That’s literally threatening the PLA with a good time.
The primary issue with American forward bases is one of distance and support. Those bases are well within range of massive amounts of PLA firepower, with so little in the way of strategic depth to manoeuvre and relocate that putting more forces there is basically the worst thing you can do since that just makes it a far more target rich environment for PLA munitions. In the modern age, when attack massively overmatches defence, no amount of additional AD or makeshift hardening is going to be able to stop the kind of overwhelming firepower the PLA can easily bring to bare, in a sustained manner.
The USN deploying more carriers will give the PLA planners a headache as those are highly mobile assets that are hard to find and keep tabs on.
But the US wanting to cram more aircraft and SAMs and troops into its forward bases around China is no threat to China at all. Even the US realises this, which is why it is investing in new bases in Australia, while at the same time trying to develop disposable unmanned long range strike capabilities to forward deploy so it can do its own alpha strike without risk loosing its fist and entire arm after throwing the first punch. But it is still only are the infancy stage with those developments. So unless and until the US makes massive progress in that regards, China can afford to let the US throw the first punch, because it is poised to rip that entire arm clean off as soon as that punch is thrown.
I cautiously agree, to an extent -- it depends on the extent and scale of the US to reinforce and harden its existing bases, not only in terms of SAMs and missile defense and EW (both land based and naval/surface combatant), but also in terms of materiel, repair equipment and redundant logistics equipment, and so on.
From the US's point of view, the ideal situation is to be able to harden and defend those bases so well such that their ability to defend them is able to prevent the PLA's strike systems from outmassing them. That, supported by a large surge deployed US carrier force operating at a distance where the PLA is less able to sortie large naval strike packages, would be naturally further supported by more distant bases (such as Australia, Hawaii) acting as more distant logistics nodes and transport hubs as well as staging areas for longer range bombers.
In such a situation, over the near future I am not sure if the PLA has the capabilities to fight and credibly win such a conflict on comprehensive terms that can lead to a negotiated peace in its favour.
Part of this is because we don't know how well the PLA's missiles can match up against US SAMs and missile defense systems in a hypothetical wartime surge/reinforced fashion, and also because we don't know just how big each strike package can be, and how many reloads the PLA has.
In absence of that information, I think erring on the edge of caution is not only prudent but necessary.