One way of ensuring a defense against early rush is Gaohan in Command. Also, in the event of Verore Kidnapper and Kidnapped By Demons removing them from play, having more Avatars in deck will help. When you get your kidnapped Avatar back you'll have 2 Unique characters in play!
That said, I realised the Exiles have many options against Avatars. Other than above, there is Demonise, Dehumanise, Wholesale Slaughter and Descent Into Madness. Verore also has Voracious Goliath. It is worth noting that Hubris is good against Avatars as unlike killing them, it will not reset their stats while making them non-threats, if only for 1 turn more.