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I cannot get it unfortunately because BK hid the replay and he is no longer in the tournament. I did watch it live. I'd enforce it but there's not really much I can do and it is not darkinium's fault so I can't really make him play the set again.
Unfortunately I don't have the replays, like you said they were made private. I tried looking through my search history to see if I could find the original battles in hopes of being redirected to the replay, but it didn't work out. I also looked up the alt I used (which was my main, Darkinium) on PS!'s replay site but couldn't find it there either, I'm not sure what you mean by "the private tabs".