After many years of looking after free range chickens I returned to the UK and took on the care of Ex Battery hens. The contrast has been an eye opener.
I have never been a fan of saddles for hens. However, I have a chicken keeping friend who has many years of experience who makes his own saddles out of leather and has had good results using them to protect a couple of his hens from mating damage to their shoulders and lower back.
Quite a few of the Ex battery hens I took on were feather pickers and eaters. But, with a couple, the feather picking was I discovered self inflicted. It is a habit they pick up, possibly to supplement their protein, possibly stress related.
Given you are in the UK finding a higher protein content feed than the standard 16%, in my experience at least, isn't easy, but it can help improve the situation.
Stress reduction can also help so plenty of room in the coop and run is helpfull.
What you do need to be aware of is hen saddles prevent the hen from dust bathing properly and grooming the areas they saddles cover so some time without the saddle during the day is important for hygine and comfort.
I have a thread mainly concerning Ex Battery and rescue chickens which you are welcome to drop into with any questions we may be able to help you with or just to chat about your experiences with your rescued hens.
https://www.backyardchickens.com/threads/shadrachs-ex-battery-and-rescued-chickens-thread.1502267/