I like the proposal as it is, but these are my opinions on what I would change, if you disagree, feel free to ignore this:
- Ax duels should not be compulsory. If a player with axes lands on a square containing other players with axes, give the player the choice whether or not to start an ax duel (and if there are multiple players there, possibly have the choice of which player to duel with)
- The proposal says nothing about what happens if the result of the ax duel is a tie. I would award ties to the defender, just to make the attacking player think twice before picking too many fights.