I found it easiest to deal with those dragon heroes by going all out on spell casting. Geyser is very useful since it deals physical damage / frost damage and at level 2 it affects enough targets to hit all enemies while mostly bypassing the magic immunity of the black dragons.
As for group lineup I'd recommend replacing the demonlogists with something melee. Ice Dragons maybe? there should be enough eggs lying around for at least half of your leadership.
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