Time for a trite, unthought-out, and already-considered-by-everyone idea:
Analogous to how the quantum foam produces particle pairs, some of which occasionally get split by asymmetric background stuff before they would have re-merged and evaporated, what if the universe is mostly unbiased but sometimes bubbles form and split off with matter/anti-matter weightings? These would be the big-bang-universes-within-a-multiverse type of thing. If we need yet more statistical massaging, it could get anthropic with only these kind of universes supporting complexity and life....
Michael
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Dammit babies, you've got to be kind.