I have a solution to this: make the hunt battle instanced. Like the quests where you have to enter an instanced area and have an instanced event there (the street fight in Ul'Dahg and the lvl 50 Summoner quest pops up in my mind). It stays there for like 10 minutes when it spawns, and you can form groups to enter.

THERE, MAGICAL SOLUTION. EVERYBODY IS HAPPY.