Ideas and suggestions.

So, regarding Overlord Hour (OH): if both players access the same object, the OH is interrupted – first, Red goes, then Blue, and the OH resumes after 3 days;

Blue sees Red's actions from the previous day (emulating a real game), and when Blue attacks, Red's turn is rolled back to that day, and the OH is interrupted for 3 days.

Red sees Blue's actions immediately on the next day.