The control of the Yellow Sea was vital for Chinese defense in Korea (roads were considered impassable) and instrumental for Japanese victory. So I would set the POD during the Battle of the Yalu River.
From Paine, S.C.M. (2003) :
The Sino-Japanese War of 1894-1895: Perception, Power, and Primacy. Cambridge University Press. pp. 179–189
Some military analysts, notably U.S. Secretary of the Navy, Hilary A. Herbert called the battle ‘nearly a draw’ – although the Chinese had lost several warships, the Japanese had suffered considerable damage, and if the Chinese ammunition had been of higher quality, the outcome might have been different.
Although the Japanese fleet was quicker, the Beiyang fleet was stronger than the Japanese fleet and had, for example, bigger guns. The main problem was lacks of live ammunition training and lack of good leadership. Their battle formation was also inadequate and they later gave command to foreign Army officer in the middle of the battle. The Chinese flagship, Dingyuan, also exploded her flying bridge, due to bad engineering (and it was known that it would happen).
The Japanese fleet had tactical advantages in their better-maintained ordnance and superior quick-fire training over the Beiyang fleet, which fought with limited stocks of bad quality and badly trained crews. A few Chinese ships on the left wing also fled before the battle.
The battle seems to be fated to be lost ? Not in my opinion, the best solution would have been to stay in the Port of Lüshunkou (Port Arthur) which was well protected and couldn't be taken without a combined land and naval attack. The idea would be to use "fleet in being".
In naval warfare, a "fleet in being" is a naval force that extends a controlling influence without ever leaving port. Were the fleet to leave port and face the enemy, it might lose in battle and no longer influence the enemy's actions, but while it remains safely in port, the enemy is forced to continually deploy forces to guard against it. A "fleet in being" can be part of a sea denial doctrine, but not one of sea control.
The Japanese naval strategy was "Jeune école", a french naval school of thought to counter the stronger British Navy with small, fast warships, especially cruisers and torpedo boats, against battleships. The best way to counter it is ... not to fight or to fight on your own field with heavy preparations in a small area.
Without a victorious naval battle on the September 17 1894, the Japanese would have been forced to slow down their operations and to concentrate on Korea. More importantly, the Japanese would have been unable to easily enter Bohai Sea and to directly threaten Beijing. The presence of the Chinese fleet in Lüshunkou also means a threat to the Japanese fleet or convoys from Korea Bay to Yellow Sea, which would force them to extend their supply lines or at least to keep them farther from their moving troops. They won't be able to make as many landings as OTL and will be more hesitant to do so.
The Japanese fleet will certainly be kept in front of Lüshunkou to guard the port which means consuming supplies and being unable to disperse your fleet. When you know that the other modernized Chinese fleets in the south are still intact and that Chinese could harass convoys later or simply threaten to do so, it will mean that the Japanese fleet will be divided and won't stay complete in front of Lüshunkou.
Of course, it won't totally butterfly the Battle of Jiuliancheng and there will be a Battle in Lüshunkou, but the Chinese will certainly get an higher morale and could focus their defenses on Weihaiwei, Dalian (not forgetting to burn the docks in TTL to deny logistics for Japan) and of course on Port Arthur.
Before Lüshunkou battle, the Beiyang Fleet had received orders from Viceroy Li Hongzhang (based in Tianjin) to withdraw to Weihaiwei rather than risk engagement with the Imperial Japanese Navy, and was thus not able to play any role in the defense of their base in OTL. ITTL, the Beiyang fleet would be complete, undamaged and able to trade fair punches with a divided Japanese fleet, while being supported by Armstrong and heavy Krupp guns coastal batteries.
A map of Port Arthur here (1905, but you get a nice idea of the topography) :
http://upload.wikimedia.org/wikipedia/commons/7/7c/Map_of_Port_Arthur.png
The OTL battle (after the Chinese defeat in Battle Yalu which didn't happen ITTL :
http://sinojapanesewar.com/PortArthur.htm
The idea is either to win Port Arthur Battles or to inflict enough casualities and losses to the Japanese to turn the land and naval battles into draws or to force the Japanese to retreat (naval either land retreat or both). Imagine if the Japanese had to retreat to Korea or simply to continue the war with a now crippled fleet having difficulties to provide good protection for their convoys. The three other modernised Chinese navies were still intact and the complete Japanese Fleet was used for the previous battle. A naval defeat and potential destruction of numerous Imperial Navy ships, alongside the casualties from the land battle will be a kick to Japanese nuts.
Korea will probably stay in Japanese hands, but it's not sure. If you get sufficiently good land commanders and the control of the waters around Korea, the morale collapse will be Japanese.
Amazing website here :
http://sinojapanesewar.com