And IRC that happened in OTL, basically the two destroyers forces found each other due to pure chance...almost ASB? Sure, but reality had plenty of times demonstrated to be unrealistic; even a little earlier a russian gunboat come near the japanese fleet transporting troops to land in Inchon, and the brief firefight seen no score from either side.
Image if the fleet is more combat ready due to the Tsar order to be more aggressive (OTL many russian officers were partying during that night), or in general if more troops and equipment are sent on the Far East before the war; sure the Russian will be understimate the Japanese but the situation in the Balkans mean that the war need to be resolved quickly or the Bezobrazov Circle decide and succeed in bring General Kuropatkin away from the Far East before the war due to his perceived reluctance in a war against Japan.
Even a month more it's something that Japan can't afford, even more if the general loss are heavier than OTL and while their hometurf advantage his great and important the limit at the resources that the nation can put on the war effort it still a very important factor
I would argue that Russia can't afford another month either. They wouldn't have accepted the humiliating peace if they were confident about turning things about.
I haven't read anything about a destroyer squadron meeting up the Japanese attackers and because of how unlikely that is, I'm not inclined to believe it. Especially since it also means that the Russian destroyers didn't react to it.
Finally, a couple of questions:
Can the Czar even give such an order in time for the fleet to be in such a stance? Arguably, the Japanese would launch their attack as soon as they realise they might lose the surprise element.
How would a Russian ship randomnly explode that would lead to then blaming the Japanese? Sounds very Maine-like, but how can that happen in these circumstances unless the Japanese really ARE behind it, meaning that it would be all part of the planned surprise attack and give the Russians even less time to react. If it's a random explosion, then why would they blame the Japanese? Unlike the Maine incident, the Russian ship wouldn't be in a Japanese port in a conflict zone heavily involving them. It would be in Port Arthur where Russians were responsible for and I doubt the other great powers would believe the story of Japanese somehow behind it. Hell, if anything, it makes Russia look like the aggressor and drags the UK against the Russians! In fact, now that I think about it, if the Russians sail out to meet the Japanese fleet before war is declared, then there is no doubt that Russia would be taken as the aggressor, activating the Anglo-Japanese alliance... which has way bigger consequences in the end. It put Russia in a much worse situation and gives Japan the financial backing it needs to prosecute the war.
Is the Russian Far Eastern Fleet even able to act if they are ordered to take aggressive actions? I don't know enough about the fleet's situation to answer this myself. Would they even bother taking the order seriously, not seeing the Japanese as a credibly threat if was hasn't been declared? What was the quality of officers in the fleet? Their commanders? Considering the failures of OTL and how they weren't to defeat the Japanese even once, I'm curious if the quality of the fleet was part of the problem.