I think a lot of this does bend the limits of credibility quite a bit. To start with, I really can't see a Japanese fishing boat with lots of Taiwanese on board, unless it was a false flag spy ship sent by Taipei (in which case, why would Japan and the US scream blue murder over it)?
Also, whilst I can see a Chinese surprise attack on Taiwan happening, having US subs in port is stretching it a bit far. If US subs were in port, China would have been kicking up a massive fuss about this on its own, if not already striking out against Taiwan.
That said....
Now: if Japan manages to pull off a major victory against the PLAN on their own, then
1) That's billions in research and development lost for China.
2) Nothing standing between enemy submarines and Chinese shipping lanes.
3) Massive loss of face for China - the navy, their most visible 'superpower' symbol, beaten by an 'inferior' enemy. This could lead to major internal issues - wouldn't take much to spin this as government incompetence.
Would they be able to continue a war in such circumstances?
...this would definitely be the case for China. Along with the whole loss of infrastructure from any direct attacks on the mainland. My guess would be that in order to appear strong and deflect internal discord / hostility to the government, some hardline Party / PLA people will start letting a few nukes fly. And then it's game over in East Asia.
Whilst I think the circumstances of the the Count's crisis leading into war list are pretty unlikely, I do think that a war is quite likely in North Korea under some circumstances, given the apparent loose grip L'il Kim has on things and I wouldn't be surprised if China uses this as smoke to cover an attack on Taiwan whilst the US, Japan and SK are otherwise engaged. Especially if the DPP wins the upcoming Taiwanese election. My take on a descent into war in East Asia would be something like this:
1. The DPP wins the 2016 Legislative Yuan and Presidential election in January
2. After winning the election, the DPP immediately sets about rewriting and pulling out of large chunks of the ECFA
3. China obviously doesn't like this and begins reinforcing costal missile batteries in Xiamen, deploys more PLAAF squadrons to southern China and sends the Liaoning on a leisurely cruise through the Taiwan Strait
4. Meanwhile, in North Korea, a military coup against the Kim regime succeeds in toppling him but is immediately countered by other interest groups from the DPRK military. Limited fighting erupts in the streets in Pyongyang
5. In response to the instability in North Korea, South Korea puts its military on the highest state of alert and readiness. US Forces in Korea follow suit
6. A Taiwanese naval vessel is sunk by a stray missile fired from the PRC as part of a live fire exercise. All hands lost
7. In response to the sinking of the navy vessel (no warnings of live fire exercises were given by the PLA), the DPP government immediately pulls out of all ECFA agreements and suspends all cross strait flights. Any flight on a Chinese airline already en-route and over the Strait are ordered to return to China or be shot down by the ROC Air Force. In China, China Airlines and EVA planes at Chinese airports are impounded, with crew and Taiwanese passengers placed in detention
8. Factional fighting in North Korea slowly spreads across the country and is widely reported as being a 'full scale' civil war by international media, who are not allowed access to the country. A pitched battle is fought within 10km of the DMZ, with some shells falling on the southern side of the border. For the moment, South Korea does not respond
9. China requires all Taiwanese citizens in China to report to their nearest police station for 'security and safety reasons'. In reality their ID is confiscated and they are placed in detention. Taiwan responds in kind; all Chinese nationals in Taiwan are rounded up and placed in detention
10. China demands that Taiwan immediately releases its citizens and allows them to return to China. Taiwan refuses unless China does likewise, which China refuses, stating that the Taiwanese in China are being protected from the danger of any military escalation. This diplomatic impasse continues for a week
11. One military faction in North Korea launches a missile that crashes into Nowon district in northern Seoul. Whilst it does not explode, it is quickly found to be holding a low-yield nuclear warhead
12. Given that the situation in North Korea does not appear to be stabilising and worried that more nukes may fly, the South Korean and US militaries cross the DMZ to stabilise the situation and try to safeguard the South
13. Elements of the PLA begin to cross the Yalu River in the north in 'support' of stabilisation
14. Fighting breaks out between US and SK forces and parts of the North Korean military
15. An urgent summit is begun between the US, China, SK and Japan. It is decided that the Chinese will work to quell the fighting up to a line drawn north of Pyongyang and the SK and US military will meet the Chinese at this line, Japan is to provide logistical support and additional air / missile defence capabilities in the South. This does not prove popular with South Korea, but the additional support is gingerly welcomed. Both sides agree not to interfere in any operations that the other side is undertaking
16. As US and Japanese logistical focus shifts onto supplying forces in the Korean peninsula, China begins to launch missiles targeted at military bases on Taiwan
17. The US and Japan protest this move, but China states that it is an 'essential part' of the regional rebalancing going on and that the US and Japan agreed not to interfere in Chinese operations. In back room negotiations, China implies that it will support some of the North Korean factions against the US and SK if the US does not keep its nose out of Taiwan
18. After the initial missile bombardment of Taiwan, a massive strike is carried out by the PLA to bomb additional military and industrial targets, as well as drawing out surviving elements of the ROC Air Force. The ROC Air Force is rapidly destroyed
19. The PLAN commences operations in the Taiwan Straits, effectively closing it to the ROC Navy. In what was seen by international observers as a stroke of luck for China, the ROC's submarines were sunk very quickly
20. After one week of fighting, US and SK forces reach Pyongyang, which was already half-destroyed by North Korean fighting. It surrenders to the forces without a fight. A couple of days later, China arrives at its side of the pre-agreed line
21. The US, SK and China agree that Korea will be reunified under SK rule and that China will effectively offer a blank cheque for North Korean rebuilding and modernisation, extending any modernisation schemes / infrastructure projects into the South as well. This is given on the understanding that the US leaves Korea within 6 months, as it is no longer required on the peninsula, as SK and China are 'allies'. SK supports the Chinese in this, so the US reluctantly accepts
I think this is more likely to be along the lines of what will happen (with longer timescales, maybe). But what would the result of this be? Would the US really agree to leave Korea and leave it in the Chinese sphere of influence? Would this provoke the US into supporting Taiwan and repelling the Chinese attack (knowing that if it did so, its forces may have to begin to fight the Chinese in Korea, who may now count the SKs as their allies on the peninsula)? Would Taiwan be left to a Chinese invasion - or would the US risk losing China and South Korea (now United Korea) as trading partners over a small island? However, it may well do so, as given that it no longer has a foothold in Korea, it needs to keep Taiwan as an option for its own military projection in the region and counter-balancing of China.
I guess the basic question is, how would the US deal with this dilemma? This would be in early 2016, so before the presidential election, so Obama would still be in the White House.