It may seem counter-intuitive, but consider adding Trick Room on Alakazam, since it has the speed to set it up. You can replace Hidden Power (if you have the TM) or Encore. Also, giving Alakazam an Amplifield Rock will give you enough Trick Room turns so that Bronzong won't have to set it up later.
You could lead with Alakazam + Bronzong. At turn 1, Alakazam can use Trick Room, which means that Bronzong attacks before Charlotte's 'mons, thereby letting you use Rain Dance before they hit you with those fire moves.