I also process my own chickens, male and female, young and old. I'm not sure if you are after how to process or how to cook an older bird, but I'll just tell you how I cook the older ones. The secret to cooking an old chicken is to cook it long and slow with plenty of moisture. Never bring the water ot a full boil, just barely to a simmer. Some people bake them, long, slow, and basting a lot.
When I process the birds, I cut them into pieces; thighs, drumsticks, breasts, and wishbone. These are to cook for direct eating. But I also save the necks, backs, wings, gizzards, heart, and feet for stock. The feet are dirty and will turn a lot of people off, but if you scald them, the toenails easily twist off and the skin peels off. I consider that plenty clean enough for me to use the feet and they add a lot to the stock. You need to get the scalding right or the skin can come off in little pieces if you over scald, but once you get it down, it works really well.
I pretty much cook the meat to eat and the stock the same way, in a crock pot. I have used a big stock pot. I put in peppercorns, a bay leaf, rough chopped onions, carrots, and celery, and whatever herbs I feel like or have on hand. That's practically always basil and oregano, often with thyme, maybe chives or garlic. Add the meat, cover with water, and cook on low maybe 8 to 9 hours. The meat can be a tad stringy but it is tender and tasty. The broth it was cooked in can be used to cook potatoes, rice, pasta, or make a soup, basically anything a stock can be used for.
For the stock, do the same thing with the stock pieces but cook longer, maybe 11 to 12 hours. Separate the fat and filter the liquid through five or six layers of cheesecloth for a tremendous broth.
I also pick the cooked meat from the wings, neck and back. This is tremendously flavored cooked chicken meat. It is a bit of a pain to pick it out since it really has pretty much cooked off the bone. You can use it for chicken tacos, salad, pasta, or any way you'd use cooked chicken meat. I often make a sandwich with it for my lunch.
This is just how I do it. There are a lot of different ways that you can cook older chickens and have them taste great.