Given the difficulties Russia had with its supply line across Asia, the only way the war can be won is to prevent the Japanese build-up of troops and supplies. This can only be done at sea. So the only possible PoDs must result in Russia dominating the naval campaign.
Some PoDs to consider are: -
1) The Russian Navy is a more competent organisation than TOL - that will have to go back years - resulting in better trained officers & men with higher morale, and a more daring & inventive approach to warfare, along with better quality ammunition. If you like, a "Whale has Wings" scenario for the Tsar.
2) Stark, in command of the Far Eastern Fleet at Port Arthur, is successful in convincing Viceroy Alexeiev of the Japanese threat, resulting in a far more alert defence fending off the surprise Japanese torpedo attack. Battleships
Retvizan &
Tsarevitch are not damaged. Alexeiev does not issue his order restricting the fleet to no more than one day's sailing from Port Arthur. It would help if the entire Russian command had not been at a party as the Japanese attacked

3) Makarov's order on 13 April as the fleet steamed out from Port Arthur that the harbour mouth be swept for mines is carried out. The
Petropavlovsk is not lost on return and Makarov survives. [I believe there is an established timeline for this.] The fleet is stronger in terms of command, material and (most importantly) morale. With a stronger mobile force to threaten Japanese lines of communication, Togo could be forced to more extreme measures to blockade Port Arthur; at the time this was a vital concern for the IJN as the Guards Division had barely started landing in Korea.
4) The Japanese lose the
Shikishima to Russian mines on 15 May in addition to
Hatsuse &
Yashima. Or a more aggressive Witgeft (or the resurrected Makarov) follows up with the available destroyers, or in the following days takes advantage of the Russian advantage in battleships to force an action or attack Japanese troop & supply convoys.
5) The ammunition explosion that sank
Mikasa at anchor on 11 September 1905 could have occurred at any time. If it had happened earlier, particularly around the loss of the two battleships mentioned above, the Russians would have had a major advantage in battleship numbers. If you want to be particularly evil, have Togo on board

6) The "lucky" hit on
Tsarevitch at the Battle of the Yellow Sea that killed Witgeft is avoided, or -even better for the Russians - transposed onto the
Mikasa, putting Togo out of action. At the time observers believed the Russians had the upper hand tactically, and it was the absolute confusion that befell the Russian battle line that decided the outcome. Ukhtomski - a "second rate man" - does not have the chance to flee unheroically from the field.
There is no point trying a PoD as late as Tsushima. The war on land had effectively been decided by the time Rozhdestvenski's Baltic Fleet arrived, and nothing short of an ASB miracle would reverse the overall result of that battle.