I also cringe at "once per fight." Sounds rather like an encounter power to me. *shivers*
I cannot think of 'once per fight' moves elsewhere but take a look at this.
Fiction dictates action, and action dictates fiction. There are a number of moves upon 'entering a new area' (rogue), entering a town (bard/rogue), per day (steading/rest).
Rogues move room to room. Bards - person to person and town to town.
Similarly: Fighters are creatures of war, fictionally moving from battle to battle.
I can see why 'encounter' bothers some people, but I think this is different, in-theme, useful and possibly appropriate in this case.