I agree it is possible that the inflamed skin could be due to a yeast infection (vent gleet).
I would also like to add that it is important for hens to have a healthy diet just like any other animals and they can get obese or suffer other health issues if they are fed too many treats routinely. Those feathers hide a lot and most chicken owners would not realise that their hens were carrying too much fat.
I would be very wary of giving them cheese and ham on a regular basis .....processed foods high in salt are not good much as they love them. If you give them some tinned fish, it is probably better in oil than brine but some raw liver occasionally might be a better option to up their protein levels along with the odd egg.
It is also important to limit the grains you give them as they will eat these in preference to their layer pellets and dilute the protein and calcium levels which again can cause reproductive issues. Soft shelled eggs, eggs getting stuck and causing the bird to prolapse, internal laying and liver haemorrhaging can all be associated with an inappropriate diet. Formulated feed is manufactured to provide hens with all the nutrients they need in a balanced ration. Once you start adding extras the balance is lost and problems can occur. The "Emergency and Diseases" section of the forum is full of birds with such problems and much of it is because we as back yard owners, love our chickens too much and are tempted to treat them too often. Treats should make up no more than 10% of their daily food intake but less is better and not every day. Meal worms are probably a much better treat than grains or cheese and ham, but again, don't over do it.
Regards
Barbara
PS. You are absolutely right.... your husband deserves a medal! He is an absolute star!