I get your feeling, we have a case in England where the NT manager recruited a 36yo player of his Play-Down opponent, which is completely unfair and not right.
Oh thank you very much. It's a real issue. Hope Lithuanian guy read this, so he stops telling me I'm ignorant
My proposition is even simpler: Just give managers the chance to put every player, just like when we sell them on the market, available or not for NT. If the Manager say yes, every "risk" is upon him, the player will be in the NT list and coach can check his skills. If he says no, then NT team will have to chose another player or contact the manager and have some good diplomacy to change things.
So you will reduce cheating chances and improve communication between managers, and maybe, lot more involvement for NT from "nobody" managers with good prospects in their team
No need to implement new rules or forbid something. Just leave the free choice to managers, just as they already have in managing all other aspects of their team.