I was asked to give my opinion as to why I don't think it's Garth. Fine.
I don't think it's Garth for the same reason why I don't think it's Gary Mitchell, Roger Corby, Ron Tracey, Harry Mudd, or any other TOS baddie that you can come up with. The target viewing audience simply would not care about this. It's purpose would only be to satisfy trufan fanwankery, and that's not necessary anymore.
I've heard the rumors too that BC is supposed to be a TOS character. I personally think that's bullshit (or at the least, he'll be a TOS character in name only). The Dark Knight Rises is a perfect example of this. While Bane was a good villain in that movie, he was completely, completely different than the Bane from the comic. But Bane was chosen for a reason: he broke Batman's back in the comic, and he broke Batman's back in the film.
So with that logic, who in Star Trek's past wanted bloodthirsty revenge against Kirk? Garth? No. Gary Mitchell? No. Harry Mudd? No.