I think this might cost more than 6... but it might not.

Let's look at comparable cards: Fumigate doesn't have the life loss (Destroy/Exile difference is secondary to that). Deadly Tempest does the life loss thing, but each player takes pain only for their own creatures.

I think you are close. I think just a multicolored Deadly Tempest could keep the life gain at the came converted mana cost, but what really worries me is that this can take out all opponents in multiplayer in one fell swoop.

Yay secret does research! if you wanna keep it this way, which i think is the most flavorful and color-appropriate, and just my biased personal fav... i guess youèd have to push it up a bit. maybe 8 :P 8 drop mythics can do next to anythign not banned lol

Exile each creature, each opponent loses X life and you gain X life, where X is the number of creatures exiled this way