I agree with you about Salinger's short stories.
The Laughing Man and
Teddy are two of the most moving (and beautifully, perfectly written) short stories I have ever read. Have you ever read his daughter's autobiography,
Dream Catcher? It created quite a bit of controversy because it portrayed him as rather self-obsessed and vain (not to mention mentally fragile), although personally I came out of it feeling closer to him and with my admiration for him undimmed. He was far from perfect, but not in any truly awful way, and there is, I feel, always something dignified about seeing somebody warts and all.
It spelled the end of their relationship, of course. The old man was fiercely protective of his privacy and did not take kindly to having the lid lifted on his home life. But his daughter definitely inherited his ability as a prose writer, and is an engaging and hugely likeable narrator too.