You might be making this too complicated.
This isn't the first time I've heard of Peter Singer, so it's possible you're just working from this one data point. Yes, the man is crazy, and yes I consider nihilistic lunatics to be poor teachers of our younger generations. I wish he was the only one in academia.
Most people who use the term "social Darwinism" as a pejorative are applying the concept incorrectly. Come to that, it's difficult to nail down an exact definition anyway. But those who know how evolution works are well aware that "survival of the fittest" does NOT always mean "survival of the largest or most powerful."
What exactly is "hyper" competition?