For me, using a support image as I described above *completely* resolves the issue that you are describing.
To the nearest that I can tell, the local support image protects the areas covered from any deconvolution (or at least significantly reduces it). For really bright stars, this seems like the best thing to do. If you want to make them smaller, the you could use MorphologicalTransformation late in processing steps after the image has been stretched. It's usually one of the last things that I do (if I'm going to do it at all).
Deconvolution works great on dimmer stars and contrast details in non-stellar structures, but my personal opinion is that I think that overly bright stars should be left alone - and the local support image works great for that, especially if the bright star is embedded in galaxy or nebula details.
YMMV.