It wouldn’t let me post a reply in this thread, but I have a suggestion:
I know one player must get a different colour, but could you not always force “the other player” to change.
Ie, so if Player A and B both pick a blue outfit; on Player A’s screen, A is blue and B is red, but on Player B’s screen B is blue and A is red.
That way, both players recognise their character as the colour they selected, without worrying about the game having two identical players on screen.
Just a thought