Play Split Fiction Local Play with 2 Different PSN in different games on PS5

My wife got Split Fiction for our 9-year-old son for his PS5 and the two of them started playing together.  They stopped after about an hour and their game was saved.  The next day he wanted to play with me (his father) and we started a new game, but we couldn't figure out how to change the controller to be set up to my PSN account instead of my wife''s.  Her PSN account was logged out of the PS5 and in the PS5 accessory settings it showed the 2 controllers assigned to my son's and my PSN accounts, but when we went into the new game Player 1 was assigned to my son's PSN user name, and Player 2 was assigned to my wife's PSN user name.  We can sign my wife out of one of the players, but there is no potion to sign me in.  We can't figure out how to change it so that my son has one Split Fiction game going with my wife and another one going with me.  WE of course would play at different times.  Is there any way to do this?  Appreciate any help.