Several Pheasant species in aviculture/captivity do suffer from inbreeding due to the low numbers of original founders. Evidently Edwards' is one of these. Inbreeding in pheasants sometimes manifests itself with twisted toes but I don't know if they suffer from this.
Lady Amherst's has a different problem, many strains are impure, due to past crossing with Golden Pheasant, sometimes very many generations ago.