Stop trying to treat the problem by feeding them eggs filled with something is rule number one. "eggs are food" is what they see.
Then provide a dark place for them to lay and a light place for them to eat so that eggs in the dark place aren't seen as food.
Cut back on everything but the commercial feed and the calcium until the problem is resolved in case it's nutritional.
Egg eating is sometimes just a habit, so if all else fails, grab a pair of wire clippers and trim a half inch off of the top half of their beeks. By the time it heals the habit will be broken.

Don't know if you're interested in building something, but you can make a nest box with a tilted floor and a slot at the back that's about 2 inches high for the egg to slide out. Put the nest box against the side of the coop and cut a hole so the slot sticks outside the coop.

If you can't put the nest box against the coop, then you have to make a double-tilt bottom to the box so the egg slides into the bottom of the box. Or have the slot in the back allow the egg to drop to the ground under the box.

In either case, might help to put a strip of old carpet or astroturf on any section the egg will strike against as it rolls.

It's never a bad idea to check if the birds are eating eggs due to missing a nutrient, but your diet sounds good. Varied. And eggs taste good, even to chickens. It's easier to remove their ability to get to the eggs than to remove their desire to eat them.

I caught my guinea 'in the act' with egg on his face. Guineas taste really good. Solved my egg problem too.

We have a similar problem with a single hen. It's under control now. I had to switch to gamebird feed - higher in protein. Whenever I switch back to layer pellets, the egg eating problem returns.
I've often heard that the habit is spurned by a protein deficiency. You could try and adjust the feed in addition to a few other strategies. Collect the eggs asap (if you can) so it interrupts the habit. We also put fake eggs in the nest boxes. The false eggs don't provide the same return as the real eggs - might help to discourage the problem. Couldn't hurt I suppose.

I've heard too that once you have an egg eater - it's time to cull. However, we turned ours around - but I have to be vigilent.

Good luck.

FYI for everyone, I heard on NPR science Friday the other day that birds can't taste spiciness so trying to discourage any kind of eating/pecking behavior with spicy substances is pointless.

As for the egg eating, I have one hen that won't eat oyster shell and as a result lays thin eggs occasionally. This egg tends to get broken when the hens try to rearrange the eggs in the nesting box. Once it's broken everyone thinks it taste great but they don't touch the other eggs. This might explain why you're only having brown eggs eaten. Could be you have one hen who's not taking advantage of the oyster shell. You could try saving old egg shells and grinding them up very fine (so that they aren't identifiable as eggshells to the chickens)and offering this to the hens. If it is a picky eater she may eat this and get the calcium she needs.

For that occasional hen that won't eat the oyster shells buy some cheap calcium tablets and grind a couple up and stir it into some layer mesh (or any feed) add just enough water to moisten the the feed to where it will stick together in a ball but will crumble apart without much effort and give it to the problamatic hen as a treat 2-3 times a week. I use this method on a Serama that lays thin shelled eggs due to her age. She also receives Magnesium and boron supplements-these tell her body how to use the calcium.

Vitamins and minerals added to you feeding regiment keeps your flock healthy and resistant to diseases.

To see the importance of adding Vits/Mins to your animals diets look at the history of captive Turkey breeding. It wasn't until the 40's that you could not have a very large flock of turkeys due to their susceptibility to diseases. Researchers discovered that when 30 different vitamins and minerals were added to their feed this problem diminished. As larger turkey farms were then possible, turkey became a cheap and plentiful product line on the grocer's shelves the year around and not just Thanksgiving.

I caught a hen trying to break an egg laid on the floor last week. I have some relatively new layers, so they deposit their eggs willy-nilly right now, but I still don't get many eggs laid on the floor. If she is starting to eat the eggs, in the pot she will go, I guess.

I would say more than likely the chickens developed a habit but if you have a rooster the rooster could actually be pecking at the eggs since they seem to eat a little shell and yolk it could be a dietary issue. Do they get enough protein? Do they get enough calcium. If they get a balanced diet and are getting enough food and there isn't a rooster. I would follow cpp6318's advice to break the habit.

I have one hen that pecks holes in eggs. At first it was just the eggs on the floor, now I'm finding them in the nests like that. One every other day or so. They get layer mash and oyster shell. If I find out which one it is, I may have to cull her. I've seen a hen trying to peck the ones on the floor but am not sure which one it is. They are all very similar.