I believe he solved them both at least temporarily, but if either Egg 1, Egg 2, Chicken 1 or Chicken 2 ceases to be true for long, then the business won't survive.
Egg 1: trading lots of shares (check, tens of million shares daily)
Egg 2: track record on trading strategy that is scalable and profitable (probably was profitable then stopped once volatility disappeared or the market changed, but definitely scalable, trading tens of millions daily).
Chicken 1: Volume-based discount (we don't know for sure, but tens of millions of shares daily is enough to qualify as a high-tier class on many houses)
Chicken 2: Clients (check, billion dollar hedge fund)
From what is written in the post it seems that they managed to solve both problems.
"Fresh out of college... trading tens of millions of shares daily for a billion-dollar hedge fund."
"The mid 2000's when I finished college..."
"My firm finally went out of business in 2010 for a number of reasons."