My suggestion for subs would be:-
As is now, at break in play, sub board goes up to notify player to come off. From this point, the free kick, goal kick is taken and play continues but the player being subbed cannot touch the ball as he is going off.
At next break in play the sub can come on.
Therefore, the team doing the sub has to play with 10 men whilst play continues in the intervening period. This would stop the last minute subs.