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A couple hours ago, I finally got a Shiny Stakataka with stats and nature that let it do the +Atk Beast Boost thing. Monkey Paw dictated that it would have the absolute minimum Def and maximum Spe, but hey, it still works.
A few minutes ago, I decided to get the second Staka in the game shiny in the hopes of trading one for a Shiny Blacephalon later. Not even 30 SRs later, it appears, also capable of +Atk Beast Boost with (slightly) better stats.
Today was a good day. Freedom feels good man.