My chickens never stop laying except for a short period, in October/November when they molt. The standard layers are older and molt hard which equals fewer eggs, but I get a few eggs from the younger hens. I live in Florida and get very few days of freezing weather and have about 8/9 hours of strong sunlight. I feed my chickens layer crumble and give them cracked corn and black oil sunflower seeds to scatch. I didn't know that cracked corn suppressed ovulation, so I will have to consider just the black oil sunflower seeds for scratch.
My game hens free range 24/7, but I know where they like to lay. They are good flyers and have plenty of places to shelter at night and are very good layers of medium sized eggs. My standard size hens free range only when I am around because we have a coyote problem and they aren't good flyers. My bantams are confined to a large coop/run because they are easy pickings for the abundant hawks. They do seem to stop laying for a longer period of time even though their molt is barely noticable, perhaps because they get less light than the free rangers.
I do stock pile eggs at times during the spring/summer because I get so many then, which I just keep in cartons in the fridge if I plan to give them away. I keep the ones I plan to use on the counter. I will have to remember the sealed container method.