Well.. This is it. It really does not get any better than this for co-op, with the exception of permadeath where you can't do this.
This makes use of a brand new tech that I found moments before recording this video.
I disable Game Over Shop in settings. (before the video)
I make sure that my respawn location is the Hyrule Castle balcony by activating the Sheikah Stone there.
I then kill player 1 so that only player 2 is alive.
After that I enter an entrance with player 2 and quickly go to the switch home menu.
I unassign the controller for player 2.
I resume the game, at which point the game will ask me to assign controllers for player 1 & 2.
I press back, which in turn removes player 2 from the game, only asking me to assign a controller to for player 1.
Because player 2 is removed, only player 1 remains, causing a Game Over.
I then very quickly press Continue before the entrance fade out has a chance to complete.
The fade out will finish after continuing, moving Player 1 to the same coordinate that the entrance was on in the previous screen.