Several issues stand out to me.
Breeds, nutrition and age are foremost in my mind.
Any change in flock dynamics (loss of birds) causes enough stress to interrupt ovulation.
Along with the nutrition aspect is frequency of feeding. While free ranging (on pristine pasture) is normally a good thing, as are table scraps, it is insufficient for modern chicken egg production. Poultry need a minimum of 38 dietary nutrients in appropriate amounts to be productive. Layer feed contains all those. If Layer feed is 15% of the intake, they are undoubtedly under nourished. A dearth of any of those nutrients can limit ovulation.
Ovulation = egg production.
Your practice of providing a complete feed once a day is insufficient. Chickens are voracious eaters. When their crop is empty, they are hungry. When they are hungry, they will eat something - be that feed, fruits/veggies, bedding, bark, rocks - whatever. I would rather the bulk of that be a nutritionally complete feed.
As nutritious as we know fruits and vegetables are, they don't contribute to nutrition for omnivores. Red Jungle fowl - ancestors of chickens - did not eat grain, nor primarily fruits and veggies. They ate animal protein, seeds and forbs.
By only providing 15% of the diet as a complete feed, they are missing the essential amino acids they need to promote ovulation. I wouldn't doubt that if you started supplementing some animal protein, you would get a boost in production from nearly half of your hens.
Some meat and fish would be a place to start. Don't eliminate those things when you give kitchen scraps.
While the wet weather may have some impact, hens' pineal gland detects light on a basis of day length, not intensity so I wouldn't blame that.
All of your flock are not the most productive breeds. Cochins, games, sebrights and silkies are among the least productive breeds. That doesn't help your situation.
Lakenvelders are OK, Polish are iffy, Jersey Giants, Crevecours, Marans and Wyandottes are a bit better. I'm not personally familiar with Ardenners but they are supposed to be fairly productive. Leghorns are your best producers. Not knowing the mix in your flock, I'd say only half are reliable egg layers. Your sex links should be productive but may fall off depending on age in relation to pure breeds.
Basically, you can choose eye candy or egg production but they don't necessarily go hand in hand.
Add the age factor and you have something else going on. If your less productive breeds are beyond their first egg season, they will fall off quickly.
Keep layer feed available all waking hours. (they won't eat at night) Give some canned mackerel as a protein boost for about a week or two till the more complete nutrition of the feed kicks in. As you replace birds, replace them with productive breeds.
Those would be Leghorns, Anconas, Minorcas, Dominiques, Hamburgs, Rocks, Redcaps, RIRs, other Mediterranean breeds like Penedesenca, Spanish, Andalusian as well as Fayoumis are very productive and you'll see a dramatic change from silkies, sebrights, games and cochins.