It worth noting that the Down Hunt should have implied a number of Rite of Succession to be held as the dragons community learnt about the kills. However, the Rite of Survival of the Fittest seems to be the first "full" rite held with an indirect contest, instead of the direct physical contest usually held. On the other hand, dragons were a lot more discreet in the early years of the Awakening. Also, it would make sense most casualties of the Down were adult young or adult dragons, not great. So maybe most of the hoards weren't hotly disputed and most rites remained low-profiles, with only a few local dragons competing (especially, since, the more successful the Down Hunt, the less dragons remains to contest...).
However, Survival of the Fittest read "Long before he appeared to the people of the modern world, Dunkelzahn became Loremaster of the dragons, with the greatest store of draconic knowledge and the accumulated lore of untold millennia."
I guess "long before" doesn't refer to the 44 days between the Awakening Day and Dunkelzahn's arrival in Denver. To me, the expression "Loremaster of the dragons" and superlative "greatest store" is already suggesting an unified title at that point. But it's not like SR books are always super accurate in their wording, so, your guess is as god as mine... Simply unifying the title from two councils, Barsaive and, say, Americas (for the aforementioned reason), could have been enough to establish the largest store ever seen in draconic history.