Perhaps it is possible to add a trial-contract to the players to a random club, for 1 week or so from the start? That way they won't be attached at least, but it might make it more likely that they sign for that specific team.
I started one of these games and had exactly the same problem when I tried to add unassigned players.
I am obviously doing something wrong but any player I add to the database only seem to show up if assigned to a team.
Perhaps it is possible to add a trial-contract to the players to a random club, for 1 week or so from the start? That way they won't be attached at least, but it might make it more likely that they sign for that specific team.