For a campaign based on rotating DMs I have found it helpful to base the campaign on a formal organization with specific goals, rather than on a group of PCs who got together to adventure.
The PCs are essentially employees for the organization and go on missions to further the organization's goals. Each time a new DM comes in, it is a new mission.
When the DMs switch, and the DM becomes a player, the introduction of the new character is easy. "Bob is on a different mission so Fred has been assigned to the squad."
Your odd mix of roles can also be addressed this way too. You can have each player make two character, representing a portion of the organization's strength. On each mission either the DM or the player can choose which character is assigned to that particular mission. This is a boon for player's who love to try new builds, and players who like to bond with a character can just stick to one.
There are also lots of good RP option here since the characters have to deal with what is basically corporate management. There are good bosses, bad bosses, plots and coups. One DM can have the jerk boss send the PCs on what was supposed to be a suicide mission. The next DM can have the party go find the previous squad who disappeared while on a seemingly easy mission. There can be a rival squad that, like Morris Day and the Time or Kobra Kai (forgive me if you do not get the references), are spoilers and annoyances for the party. They are cruel competitors and, depending on RP, there is a lot of bad blood, but since they are coworkers the party cannot just attack them.
The Dragonmarked Houses in Eberron are good for this.
Edit: added paragraph breaks to prevent the "wall of text"
