One technique I have used a few times is to do a MaskedStretch, use RangeSelection to build a slightly blurred mask of the saturated star cores and then copy the star cores from a HT stretched image. You need to match the MS and HT stretches, of course, but that's not hard if you do the HT stretch first then read out the mean value of a background preview with Statistics and use that preview and value as the background target for MS.
Cheers,
Rick.