While I've only heard of (and treated) cushings in dogs and horses, I don't think it's beyond the realms of possibility to think that it could be found in goats. However the symptoms of cushings usually involve changes in fat distribution, drinking and urinating more as well as possible coat changes, and is usually found in much older animals.
As above, I think there may be a combination of factors, likelihood there is some scarring from the previous pneumonia, and some mineral deficiencies (imo this is most likely the cause of a poor coat) I would suggest you could ask your vet to blood sample for deficiencies or give a drench or bolus containing copper, selenium and cobalt. The scarring in the lungs may well be irreversible at this stage but will require long term consideration and being very quick to identify any further bouts of pneumonia to prevent further damage. You say your worm egg counts were clear which is great, but do you know if they checked for coccidia and fluke? Either of these could also be knocking him back.
Good luck with getting him perked up