If I were you
Our family egg consumption would blow you away, but all irrelevant info aside, I should still be getting a few eggs from our flock and there hasn't been a single egg laid in 2 months, that's my concern. Thanks for your advice.
must have a lot of boys. I think a black hole could be filled easier than filling the stomach of a growing boy.
Feathers are are around 80% protein, eggs are around 10% protein. When chickens molt there is an outrageous demand for protein. egg laying is suspended due to the protein demands of the new feather growth. A chicken does not lay an egg every day. It seems as though they do but it is closer to 26 hours which is why they lay eggs later each day until they miss a day. after laying an egg to release a new egg into production the hens eye must receive 2 hours of light to start the process. when chickens go into molt usually in late summer by the time they completely regrow their feather the days are shortening and there is inadequate light.
If I were caught somewhere in between a rock and a hard place and had your facilities, I think I would do something like this.
I would start feeding the birds a higher protein feed. I'd also make sure a good part of their diet is made up of some sort of animal protein. I would then set up a few solared powered lights inside the coop. This would ensure extended laying into the winter once they come out of molt. The downside of extended production is that the hens burn out and are pretty much spent after 2 years of laying.
I would divide y flock into 3 groups of hens (no roosters) by age and use 3 of the four coops. The 4th coop would be a grow out for pullets. Each year hatch out 30-40 eggs in an incubator to replace the oldest group once the pullets start laying.
I would set up a spiral breeding program by building 3 breeding pens. Chose the 3 best roosters, chunk one to a pen. Find the 6 best hens, chunk 2 each into each of the pens. if you set eggs from these girls every 6 days, you would have your quota for the year in 2 sets. By manipulating the hatch date to mid summer the pullets will be just starting to lay in fall and with extended lighting in the coop should lay pretty much all winter for you. Convert cockerels to capons and they can be can be housed with the flock with no aggression or mating competition. research spiral breeding programs. When managed correctly they can provide quality chickens without going outside your flock for new blood and without inbreeding depression for years.
Every year 1/3 of the flock is routinely harvested once the newbies start laying. This gives you roasters, sausage,soup and whatever your imagination can create for your family. At your level I think your gonna have to have a syste of some sort to be successful and not be throwing good money after bad. I would also look at force molting one third of the flock on my schedule rather than nature's. Originally it was a cruel and barbaric process nearly starving the birds. They found out that just by feeding them very low protein 'fluff' force molting could be accomplished humanely.
Here's something to consider. Keep your flock confined to the coops until early afternoon. By that time most of thos that are going to lay will have done so and the eggs will be in the coop rather than hidden and wasted. At your numbers this is more of a backyard business rather than a backyard hobby, at least imo.