As you stated or implied, Rain of Fire and other mass creature control spells are the bane of this deck. Dragons have enough health to survive these assaults, giving you a shot at victory.
Additionally, once you have the defense set up, you will most likely win; a cheaper offense doesn't add a whole lot to the power of this deck. You can easily cast any of the 3 kinds of dragons you want in this deck (I'm eyeballing the amount quanta you have in your screenshot), which have a lot of vitality and deal a good amount of offense.
Empathic Bonds will provide more than enough healing for you, provided that your setup is sound.