Have you tried addressing the hatred from the second personality as a separate issue? It's not as though it has a useful motivating effect, and my experience is that self-hatred is distracting and debilitating to a much greater extent than other sorts of intrusive thought.

Yes. I've been able to (temporarily) reduce it, mostly through anti-depressants and acceptance-based techniques. At my most successful, I was happily apathetic and really enjoyed staring at a wall. Alternatively, exercise channels the aggression outward, but as I'm not trying to eventually punch someone in the face, it's not helpful.

I've also tried paying attention to the amplification, which is how I originally noticed that this is happening in the first place. I saw from looking at my chat logs and similar data that I was going through fairly regular cycles of one side being dominant or the other, with a period of about 3 months. (I suspected being bipolar based on that, but I'm not particularly manic or get much of an emotional change, nor did any typical bipolar treatment do anything.)

Unfortunately, I can now totally see one side starting to take over, but not do anything about it. I can exert willpower to postpone it, but not for long.