So what do we do to bring back labor's share of income? We wait. The Great Labor Dump can only happen once. When it's over - when insanely huge amounts of investment in China have saturated that country with capital, for example - labor's share will bounce back.
I hear phrases like "the hollowing out of the middle class", and I wonder what causes that. As mentioned in the post, there a few theories, and people are trying to figure out what's going on. It might be [primarily] an effect of the end of the Cold War era trade regime. We'll see.