I don't think the game needs a healer, or a DPS. That sounds like more taking the fight to the monster than there ought to be, and it's the tank-healer-DPS structure probably doesn't need to be there when you're just trying to stall the monster and run away. Although the idea of a character who can effectively disable the monster (long stun or teleport or something) sounds cool, I think that might make encounters a contest of skill rather than just something the adventurers always want to avoid, and kind of muddle the hide-and-seek element.
On what WOULD work for making the team work together, I'm not sure, it seems like right now you want to stay separated so only one of you can die at once. Maybe multi-person wards, or buffs like increased speed/invisibility that can only be cast on other players.
That's an interesting concept. What if there was an illusionist who allowed the Wardens to disappear and escape the monster? Extending that, what if there were several more classes and all of the classes (both new and existing) were split into supporting one strategy: half for hiding, half for fighting? That way the Wardens would have both options, but be forced to choose between them, and the monster would have another element of uncertainty: just as the players don't know what form the monster is, the monster doesn't know the Wardens' strategy.
Group A (classes like the tank, healer, and DPS) fight the monster directly. They're able to stay alive well enough that it isn't a guaranteed suicide mission, but it's still very dangerous. Group B (classes like the seer, illusionist, and something else) evade the monster. They stay alive by hiding and trickery. Depending on how difficult playing the monster is, there could be a randomly selected leader each round who determines which group of classes they play as.
EDIT: Would either tomorrow (Tuesday) at 5:00 PM PST (8:00 PM EST) or Wednesday at the same time work for you guys?