I hate to suggest something so similar to another set build, but I have always felt that Firebird should be "Shoot Fire EVERYWHERE, burn everything indiscriminately and run about like a madman cackling with Glee until you get stomped and have to revive like a Phoenix". Having to be much more calculating about ensuring each mob gets hit by 3 different spells just to ensure endless burning seems like it requires too much thought. On the otherhand, if the buff was moved to the player, like Tal Rasha, then 1 Fire spell gives you a buff that applies 1000% fire damage to everything you hit, 2 = 2000% and on the 3rd fire spell anything you with with any fire spell get 3000% and burns until it dies, and you get a nifty aura that reduces damage taken.
You get to keep the "you must use 3 fire spells" but you don't have to be so conscious about what you hit with what spell.