To be honest I have no idea what is logic behind your calculations. There is no 0.005 moles of Na2A, as you still have plenty of HA- present in the solution.
You are definitely overcomplicating things. No need to use HH equation twice. Just assume first neutralization goes to completion and the only thing that matters for pH is the A2-/HA- ratio. That's what they did and how they got 1.106 g.