What a ride, thank you for all your hard work.
So the thing in the box that presumably also caused the time slip was Nobunaga's bone, specifically from the Honnoji incident... That is quite interesting, I didn't expect it but it's certainly an item of great importance.
Perhaps the regret from Nobunaga's crushed future was strong enough that when it reached Ken it could slip him back in time to right what went wrong. The world seems to be governed by a flow of history that corrects itself, you can change some things, but some things are fated to be. You need big enough push from the baseline to reach a new timeline.
Kind of like how Steins Gate works, wait it's actually just like Steins Gate!
Seems that Nobunaga and Ken were fated to be together, and his bone from Honnoji had enough pull to bring Ken back in time and gift them all a brand new unwritten future. Perhaps history will still correct itself somehow and modern day will still look the same, but I doubt that, I think it will be a brand new world. In the end none of these questions need answers, time travel is time travel and just suits the story, but it's fun to ponder about it all.