Dominoes.

Instead of rolling dice or flipping cards, draw dominoes.

Each domino can be read in two ways.  The 2:3, for example, can be 23 or 32.

Highest domino wins the conflict.  Lowest wins narration rights.

Note that you can read the same domino different ways for the two contests.  To take a simple example, if a player draws the 1:5 and the producer draws the 2:3, the player wins both the conflict and narration rights - 51 is higher than 32, and 15 is lower than 23.

The main benefit of this method is that, because each domino is different, it eliminates ties.  I find most tie-break methods a touch inelegant.