I have an elderly spaniel x from Ireland who we think had distemper as a puppy. He has classic and very severe "hard pad" (hyperkeratosis) so I have done a bit of research on it. If you're very worried, you could ask your vet about doing a biopsy as that could help establish the cause. Zinc deficiency is one, although the fact that three out of four dogs have developed it at the same time points, perhaps, to an environmental trigger?
Treatment for Tangle, after he was sedated to trim the excess growth from his feet, is foot-dips in Hibiscrub which helps clean and soften the pads, then lashings of Dermasol. To stop him licking them, I put Tuff-Wear socks on secured with plaster strip. They are breathable, so I leave them on quite a lot of the time and he even wears them for walks. He finds walking on stoney ground very difficult. Just about to invest in some Walker boots, which are fleece lined and I hope will be even more comfortable for him.
Jemima