I'd like to see a more radical alternative for Japan...so here's my suggestion.
History proceeds as normal with the Mongols conquering northern China in 1259. However then history changes when a fire breaks out on the docks while the Mongols prepare to launch their (historic) invasion of Japan in 1274. The fire burns for a number of days, fueled by the oil, pitch and tar used in ship construction. The fire (which greatly angers the Mongol lords) is eventually put out when a typhoon sweeps through the area (to the great relief of the Mongol lords), the Mongol fleet is repaired and sets sail for Kyushu.
The fire-induced delay prevents the Mongol fleet from being destroyed in the typhoon and allows the Mongols to successfully land on Kyushu. The Japanese fight with fantatical courage, tens of thousands of Samurai (who's style of war has become rigid and non-adaptive due to centuries of isolation) are killed opposing the technically more advanced Mongol troops
(Samurai steps forward, recites his lineage and challenges Mongol warrior to combat, Mongol troops laugh and turn Samurai into arrow pincushion).
The invasion of Kyushu is followed by the second (also historic) Mongol invasion in 1281 (which is also hit by storms but lands successfully due to Mongol-held beaches and ports) leading to the total conquest of Japan by the Mongols and the destruction of the Kamakura Shogunate. In a defiant final stand the Emperor himself is killed, but a group of loyal retainers secretly escape with his heir, fleeing into the woods and mountains where they join with the remenants of the Samurai and their retainers.
The majority of the Mongol troops leave due to problems in China, leaving only a small presence to maintain their authority, fight off raids by Samurai turned Ronin and ensure tribute is paid to the Khan.
In 1333 a devastating earthquake hits the eastern seaboard of Japan. Kyoto, Edo and dozens of other major towns and villages are flattened, fires consume the wood and paper buildings, there is widespread chaos and disorder.
Taking the earchquake as a sign from the gods, the Son of Heaven, Emperor Go-Daigo, rallies his Ronin troops and emerges from the mountains to take the battle to the disorganised Mongol occupation forces. Defeating a number of isolated Mongol outposts Emperor Go-Daigo rallies the people as he travels across his occupied realm before staging a grand battle on the fields of Kanagawa province. The Son of Heaven has spent his time in hiding well, learning the tactics and weapons of his enemies and the Battle of Kanagawa leads to a devastating defeat for the main Mongol force in Japan.
News of the return of the immortal Emperor sweeps across the islands and the people rise up across the land, slaughtering the Mongols wherever they are found.
Emperor Go-Daigo re-enters Kyoto and re-establishes his direct rule over the islands. The invasions and occupation had virtually anihilated the upper levels of pre-invasion Japan and only the oldest of Japanese subjects remembers what it was to live free of the Mongols. This allows the Emperor to appoint his favoured followers to positions of power across the land.
News of the uprising in Japan reaches the Mongols, who resolve to send a new fleet. However, the Mongols troubles in mainland Asia are considerable and only a small fleet can be dispatched.
Emperor Go-Daigo, learning of the Mongol's plan, sends out a call across the realm, gathering every vessel he can. Fishing craft, the remenants of the Mongol fleet and huge ocean-going Junks (which had travelled from Mongol occupied China to Japan before the uprising) and other craft are massed into a ramshackle fleet and move out to oppose the Mongol fleet.
In a desperate battle in the Sea of Japan the fleet of the Emperor overcomes the Mongol fleet. Brave Japanese volunteers set their ships ablaze and direct them into the heart of the Mongol fleet, staying at the helm and meeting their own deaths to protect their land and the divine Emperor.
The destruction of their fleet leads the Mongols to abandon plans to return to the troublesome Japanese islands.
Emperor Go-Daigo, having defeated his enemies and placed his followers in all positions of power, rules with a strong hand, breaking with tradition and intervening directly in the governing of Japan.
Never again! proclaims the Emperor, never again will foreign troops set foot on the sacred islands. The Emperor proclaims that the realm was punished by the inwardness of the Shoguns, who had allowed their infighting to weaken the realm and endanger the Son of Heaven. The Emperor decrees that Japan will build a mighty fleet the likes of which the world has never seen to ensure that no enemy warrior ever reaches the home islands again.
So that's it for background. Shoot forward to 1419 and Japan is moving forward. Recovering from the earthquake and the expulsion of the Mongol overlords has taken considerable time, as has the establishment of the Emperor's followers in their new positions. However, now Japan is strong and united again, has a fairly strong and ever-growing fleet and is determined to expand its reach and power.
How does that grab you?