Very interesting result, Ray. I've often wondered what contributes to star bloat and halos.
What effect does the brightness of the star have? Does it have the same proportional effect on the centre and the skirts?
Have you thought about applying a non-linear stretch, say a PI style MTF stretch, to your results and then plotting a linear result?
BTW, those stars look pretty soft to me... though the log scale helps
Cheers,
Rick.