I think that dissociation into partially charged ions is the 'correct' incorrect behaviour using standard functionals - see
'@article{ruzsinszky2006spurious,
title={Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals},
author={Ruzsinszky, Adrienn and Perdew, John P and Csonka, G{\'a}bor I and Vydrov, Oleg A and Scuseria, Gustavo E},
journal={The Journal of chemical physics},
volume={125},
number={19},
pages={194112},
year={2006},
publisher={AIP Publishing}
}'
for instance.
Also, it is quite hard to converge wavefunctions for the stretched molecule - I'm not sure your set up really converges. I suspect that Gaussian converges to a different solution - though you don't say what setup you are using there.
So, actually what you are trying to do is quite difficult, rather than an easy task. A better approach is to model the NaCl molecule near equilibrium then calculate the Na and Cl atoms separately for most thermodynamic applications.
Matt