Black - Destroyer of Worlds(fits well with the ambition of the Sheaim)
I'm not sure if they should start with the dragons and the religons. Building the dragon, and focusing on the dragon religion, should still be a choice the player can make. It would most likely be the best chocie to get the most out of your civilization, but I don't think he should be forced into the Dragon Cult playstyle if he doesn't want to. Perhaps the technologies could be placed a bit after Polytheism, so you could still grab them, and the dragon, reasonably early.
I don't think it should be restricted for the Kuriotates to become Black Dragon Cultists, in fact it could well be imagined that they would be compelled to do so after the death of their own dragon. Perhaps restricted while the dragon exists? And then also from picking any other religions as state religions? Perhaps the dragon leaves you if you do, and so will essentially be a religious hero.
I think the two religions should be mutually exclusive in the same city, like the Veil and the Order.
I like the idea of the dragon growing with the religion spread(it should obviously be scaled after map size in some way). It would also be possible to make it the other way around, so the religion grew in spread rate and bonuses as the dragon grew(for example, the possibility of Temple Upgrades would come at a late growth stage). But then there would still be the issue of growth. Perhaps the Gold dragon will grow through projects(requiring a good production base, which the Kuriotates will be likely to have), while the Black would instead grow by defeating enemies in combat, reaching a certain lvl of xp to grow? Barbarians shouldn't count. This would force the Black Dragon Cultists to play quite agressively, but on the flip side they'd be able to grow their dragon earlier than the Kuriotates through diligent use of the young dragon in battle.