Andy,
I find that clouds work very well and they're widely available
Bad jokes aside, I think that star removal is an inherently difficult problem and one that doesn't lend itself to simple automation. Stars vary widely in size (and even shape on a bad night), in brightness and they appear in a range of dark and light backgrounds.
What works for me is a carefully tuned star mask in PixInsight, sometimes using PixelMath to combine small and large scale masks. Getting that right is the hard part. Once I have a good mask the rest is easy - just use one of the wavelet tools to remove small scale detail (MMT or ATWT) and maybe a MorphologicalTransformation to clean up afterwards.
Cheers,
Rick.