I don't think China is out of the clear yet, most of the challenge that I listed are hard to ignore, if China decide to deal with it with military force then it will get painted as the aggressor no matter who its at fault, and if China don't react it will only embolden the enemies as they take even more actions.
China will always face problems so long as America has the military capabilities to post a threat to China. It's in their nature that they just cannot cope with anyone else being independent enough to have their own opinion and strong enough that the US cannot slap them around as and when it feels like, as has happened innumerable times throughout its short existence. Syria, Iraq and Afghanistan merely being the most recent examples. But that is a very different discussion best left unsaid for now.
When you are cornered by a bunch of school yard bully, the best strategy is to pick the weakest one and beat him up badly in front of others, so everyone will back off.
The strategy you described will work. There are plenty of smart people who think China could really use a small, high-intensity and high-tech war to add the proverbial stick to its diplomatic Arsenal, which has thus far been lacking.
Most of the countries making trouble will fall in line neat as you like if China beat the living daylights out of someone, thus showing it has both the military capability and political will to use said military when pushed.
The problem is that such an opportunity has simply not arosen.
It's fairly easy to find a pretext if you really want to fight a war, however, because the western media is absolutely going to be against China. China need an ironclad case for war that even he western media cannot spin as China's fault convincingly, but no one has thus far been stupid enough to push China far enough for that to happen.
Probably because China has done a very good job of educating others just what a bad idea that is in decades past.
India came close recently, but China was/is pre-occupied with Korea, and frankly, the scale of the Indian transgressions is simply too small for China to want to bother.
Killing a few dozen or even few hundred Indian grunts won't achieve the kind of goals China needs from such a war. It either needs to be on a scale of a re-run of 1962 (but that would require China to divert too much resources and risk tempting Trump to see that as an opportunity to start something in Korea), or naval engagement with a top naval force.
I think if they could choose, the PLA would prefer a naval engagement, as it can comfortably take out a USN CSG sized hostile fleet with minimal to no loss on its home turf, which will create the kind of impact it needs while minimising the risk of uncontrolled escalation.
India and Japan best tread carefully in the SCS is my advice to them.
However, if there is ever an universal truth when it comes to war, it is that war, no matter how well executed and planned, always have unintended consequences. One should always stand ready to fight to defend oneself and one's own interests. However, only the foolish would actively court conflict.
Just look at America. All its recent wars of choice have gone badly for them, and always produced results very different from what they originally wanted.
China's own recent history provides a similar conclusion. When China was fighting because it was genuinely threatened, the outcomes tended to be positive (Korea, India, Russia). However, wars of choice tended to be less beneficial (Vietnam), and tended to have negative unintended consequences (current Vietnamese boldness).
Or Maybe China is smart enough to indirectly threaten each of those country's other core interest for them to back off, either way something has to be done.
It's more nuanced than just threatening, it's a combined carrot and stick approach, with heavier emphasis on the carrot.
A game of chess and weiqi is being played right now, let's see if China can out maneuver their enemies without firing a shot, I have confidence they can achieve this.
Indeed, a new great game is afoot, and has been for decades. We can only see a tiny fraction of what is going on, but even from that tiny glimpse, it's pretty obvious to see that China is winning.
