I have had a call from the vet after the autopsy. Apparently it was amazing he lived so long. He had a massive infection of the lungs and heart, pleurisy in fact, and his chest cavity was full of pus. His stomach was adhering to his liver. The vet doubted that any dosage of antibiotic would have saved him, and said it must have started long before he came to me. The only surprising thing was that he also had a bad case of worms, despite being dewormed twice, and that lowered his immunity. Basically, there was probably nothing else I could have done, which makes me feel a little better, though I cannot understand how five vets missed such a huge problem.
There should be no danger to the others, though I am going to monitor them carefully (as if I don't!) and give them all an extra dose of wormer.
I don't know what I have learned from this - though there is one thing I will note carefully. That is that I thought he smelled bad - his fur and skin. I did not really take it seriously and never mentioned it to a vet, though it is something I thought vets were trained to look for.