The noise due to the Heisenberg uncertainty principle would only become "visible" when all of the classical noise sources are reduced such that the classical contribution to delta x * delta y is less than hbar / 2. I don't think this experiment reached such levels of precision
You would improve your counting statistics somewhat with 1000 particles*, but basically you'd just resolve the Gaussian distribution more clearly. The uncertainty of the measurement comes from the width of the Gaussian, and it's not like measuring more points is going to somehow make that distribution skinnier.
*(a hilariously, impossibly small number in quantum world, where photons come in doses of 10^20/second, or electrons come as 10^18/second)