Roger,
A very quick & dirty attempt at processing in PI... not sure it's a huge improvement but it's different
I was too lazy to do much with the stars but given more time I would have done some deconvolution to make the sizes similar in R, G & B to reduce the halos. Another trick I probably would have tried would be to split the image into L*a*b* and use a star mask to blur the a and b components. That smudges the star colour a bit and can reduce halos and colour up the white centre a bit.
If you're interested I can list the steps.
Cheers,
Rick.