Did this production drop happen at a stroke or was it a gradual decrease over a few weeks?
The standard reason for a serious drop in egg production is the molt. You saw the typical molt in the fall caused by the days getting shorter (well technically the nights getting longer). You have extended the lights to keep them laying but has something happened with that to make them think the nights are getting longer? You said they were not stressed but it may be something you didn't see. Stress can cause a molt or mini-molt. Basically are you seeing excess feathers flying around to suggest a molt even though it is out of season?
There is such a thing as too much light. Light is pretty important in egg laying. It's not just length of day related to molt. Light helps trigger when a hen releases a yolk to start the egg going through her internal egg-making factory. That's to prevent her needing to lay an egg at night when she is on the roost. And just like people they need downtime at night to regroup. Also just like people, some need more downtime than others. Since my chickens lay pretty well in winter when the daylight is only 10 hours or so (I do not supplement lights) I'm not going to tell you a minimum or maximum amount of light or dark they need.
Yours molted last fall so that eliminated another possible issue. If hens are kept laying constantly for a long time without a break (13 to 18 months usually) production drops significantly and you can get egg quality problems. That's why commercial operations have to either molt their flock or replace them on a regular basis. With yours that is not an issue since they molted.
As others mentioned a common reason for a drop in production is them hiding eggs. When I have a hen stop laying in the nest and hide a nest, it's almost always one hen, on occasion two. It's not 80% of the flock. Usually I would not expect this to account for the kind of drop you are getting unless something really scared them from laying in the nests. From what you described this does not sound like a real problem. They can be pretty creative in hiding a nest but at most this is a minor contributor.
You said you had an egg eater. When I had one it was only one hen. She'd open one or two eggs a day and a couple of the other hens would help her eat them. Luckily they never learned to open an egg themselves before I figured out which one was opening them and I ate her. They may eat the egg shell but usually a few pieces were left behind. And I found some soggy damp spots in the nests. It's quite possible others have learned to open an egg and this situation has exploded. To me this is a prime suspect.
Mos critters that eat eggs leave traces, usually egg shells but maybe damp spots. The hens can clean up the egg shells but often they don't. Raccoons, skunks, and possum generally leave traces. While any of these critters can come anytime day or night, they are generally more active at night. I'm guessing this would happen during the day? These critters are way down on my list.
The critters that typically take eggs without leaving any evidence are snakes, canines, and humans. I've had experience with snakes. A snake will eat a certain number of eggs, depending on its size, then disappear for two or three days to digest them before it comes back for more. I had a 5' rat snake eat 4 at a time. So if this is an everyday thing I seriously doubt it is a snake. Or even several snakes. They are not that regular.
A fox or coyote would probably be more interested in your chickens than the eggs so I doubt it is one of them. A dog however (yours or another one) may eat eggs and not bother the chickens. Growing up we called these dogs biscuit eaters. So does a dog have access?
I'll let you think about whether it could be a human.
A broody hen does not lay eggs but I'd guess you'd know if that was what was going on.
A normal laying cycle is that the pullets often lay through their first winter and keep laying until the next fall when they have their first adult molt. So they are typically a year and a half old when they have their first adult molt. The they come back and lay really well after that first adult molt until the second adult molt, which would have been last fall for you. After that second adult molt production normally drops a little, say 15% to 20% flock wide. Each individual is different, some drop more than 20%, some hardly drop at all. You have to have enough for averages to mean much, which you kind of don't, but from how many you do have I really would not expect production to drop that much because of age. You may be unlucky and have more than your fair share of nonproductive hens but that kind if drop would be excessive.
Usually I'd suggest for you to lock them in the coop or coop/run for a couple of days if you can to see what happens to egg production. If egg production goes up then either they are hiding a nest or you are locking out something that eats the eggs. Sounds like you are doing this because of that dog. You can always mark a few eggs and leave them down there to see if they disappear. That would tell you something. That game cam might be really interesting.