Chickens have been feeding themselves when free ranging for thousands of years, even before they were domesticated. They lay eggs and hatch and raise chicks. Dad had chickens like that, the only time he purposely fed them was in winter when snow was on the ground. We ate a lot of eggs and chicken meat too. The eggs may not have all been double extra huge but they were decent size and a fair amount of them. The chicks that hatched from those eggs were healthy.
To do that you need quality forage, which you find on a lot of small farms. A variety of grasses and other plants, plants going to seed, bugs, and other creepy crawlies. It can help if you are feeding other animals where they can get to their feed but it is not necessary. I grew up on one of those farms. If all you have is a manicured lawn with nothing but cut grass it will not work. I don't know what your forage looks like but what you are doing doesn't sound that unusual to me.
I don't see anything wrong with 16% Layer feed. As much as yours forage they are going to determine how much total protein they eat anyway. Lots of us feed 16% protein feed and do great.
You say they stopped laying. How well were they laying before they practically stopped?
It sounds like you are keeping them confined at least part of the week. Do you see any change in egg laying when they are confined? If they were hiding a nest (and it is not where they are confined) egg production should go up when they are confined. Sometimes critters can be eating the eggs. Most critters leave evidence behind when they eat eggs, eggshell or wet spots. Are you seeing those? Critters that don't leave evidence in Florida would be snakes, canines, and humans. Snakes tend to eat eggs one day and stay away two or three days while they digest them so if it is steady it isn't likely a snake. Most canines like fox or coyote would probably be more interested in your chickens than the eggs but a dog often will leave the chickens alone and eat eggs. Does a dog have access? A human does not necessarily mean a stranger or a thief. Sometimes it is a family member playing a practical joke.
Another possibility is that they are molting. Are you seeing feathers flying around? I know it is not the normal molting time in the fall but a drop in daylight hours can trigger a molt. That might mean a security light that went out or something like that. Stress like going without water for a couple of days or a predator attack might trigger a molt, either full or partial.
Another one is that some diseases can stop egg laying. If they are acting normal and not showing signs of disease this probably not the cause but I have to mention it.
Another cause of the stopping laying is that they go broody. I can't imagine ten or eleven of yours going broody and you not mentioning it.
I don't know why so many of yours stopped laying. There are a lot of possibilities. I sincerely do not think feed is the culprit. If you kept them confined where they cannot forage and they depend on you for all they eat it would be a different situation.