Melee DPS doesn't necessarily have to "tank it", Chirada doesn't do a lot of damage other than her skills, Slipstream (dodge it), Friction (dodge it). Downburst is the only threat to DPS which can be mitigated a lot when all 4 dps stack together.

I've done this a lot and I say if you know you're stuff, you won't be having problems with your positional skills, especially since you'll be busy using LB1 on Chirada anyway. Also note, after Chirada is dead, Suprana doesn't cast Wicked Wheel anymore.

To put it to perspective, this is very very similar to how DPS/healers used to take Chirada in Garuda HM, only this time, DPS has to be right at the edge of the tornado else Stacks can go up when Garuda and Suprana switches.