^ The basics are accurate. It sounds complex but when you play through the story as chronologically as possible, it makes sense. The fun part is that future events lead to past events, which then become precursors to later events...
In the game, the J looks as in the episode/calendar except for two differences: the ship name/registry is to the left and right of the dorsal globe (rather than above the deflector dish), and the registry says "NCC-1701-J" (rather than NCC-1701 as on the original model).
The aspect that sets the Battle of Procyon V apart from other battles is that multiple factions travel to and from it, from anywhere between the 22nd-31st centuries. As a result, the battle is in constant "replay" and needs constant interference. From the perspective of Captain Dax, her ship and fleet fight the battle, win, day over. For factions of the Temporal Cold War, it never ends.
In the game, the J looks as in the episode/calendar except for two differences: the ship name/registry is to the left and right of the dorsal globe (rather than above the deflector dish), and the registry says "NCC-1701-J" (rather than NCC-1701 as on the original model).
The aspect that sets the Battle of Procyon V apart from other battles is that multiple factions travel to and from it, from anywhere between the 22nd-31st centuries. As a result, the battle is in constant "replay" and needs constant interference. From the perspective of Captain Dax, her ship and fleet fight the battle, win, day over. For factions of the Temporal Cold War, it never ends.