At last we're happy with this. Inspired by Fred V, we went starless, separating each channel into stars and background. Colour balanced and wavelet sharpened the background. Then dropped in the original H-alpha stars as white.
To go starless, we used a dual approach: (1) model the bright core as radially symmetric about a centroid, and remove that. (2) Use multiple linear regression (3rd order polynomial with cross products) to model what should be "under" the star from the background, and feather heavily. (speaking of which, the 3 chooks are still laying an egg a day each).
The nebulosity is pretty much as before, but the stars are far less intrusive. They're all there, but smaller, fainter, and slightly better resolved.
Time to put our pen down on this one.
Original image here.
One vague possibility with this sort of approach is to try to guestimate the star's plausible temperature and therefore colour from the OIII to H-alpha ratio. Something for one of those rare rainy days perhaps.
Best,
M & T