This is probably going to be some of the most unconventional advice on here, but I've taken it upon myself to watch my chickens, learn the ways they interact with each other, and to train them. I grew up with dogs, and spent a couple of years living with a dog trainer that taught me a fair amount about dog psychology, and also watched the Dog Whisperer a lot during that time. I spend a LOT of time with my chickens, one-on-one, and group training. What do I train them to do? Just be decent, polite animals. My roosters don't crow, my hens don't make a whole lot of noise while laying, everyone's just fine with a new chicken in the group and don't try to peck or dominate... and I used to rescue chickens, too, until the risk of homelessness became too great. Now I only have three pullets and two roosters - and one of those roosters is a bantam. We're getting ready to shove off here pretty soon.
Anyway, one of my pullets, an Ameraucana ( Ziggy ), started eating my other pullet's ( Faust ) eggs! Faust lays these gorgeous, big, brown eggs. Her father was a Welsummer, so I think that's where she gets her egg colour and size from. Before I knew who was eating the eggs, though, I took one of Faust's eggs and set it in the coop. Ziggy was on it in an instant. As soon as Ziggy pecked it, I took my index finger and gave her a strong poke right on the head - as if another chicken were pecking her to correct her. Each time she went for the egg, I poked her. You don't want to use your fingernail or to make them jump or scream, just the tip of your finger. Simply the act of touching in that sharp "pecking" manner will get their attention, and it's how chickens tell each other "NO!", so they entirely understand the premise of what's being said! Now, your chickens might at first be confused by the action because they'll be wondering why YOU are pecking them! After all, you didn't used to peck them, so why have you begun pecking? However, chickens are smart, and they pick up on patterns quickly. Start with each time they peck the egg, and move forward so that if they so much as SHOW INTEREST in the egg, they get "pecked"! It took me just a few minutes for Ziggy to understand that being "pecked" was associated with the egg, and to avoid the egg, and only took me a few days before I could set one of Faust's eggs in the coop with no one paying it any mind at all. Still, if I leave an egg in there for the whole day, it's pretty likely that I won't find it at the end of the day... just means I need to spend a little more time reinforcing this!
Something else convenient about chickens is that they're capable of slightly more abstract thought than dogs, so one other way I would enforce to Ziggy that Faust's eggs are NOT for eating is to "peck" her WITH the egg. This enforces that the EGG is not to be messed with. I ONLY did this a couple of times to start out with, though, as associating tools with discipline is a bad idea for ANY sort of training.
This method of approaching the egg-eating issue will take time and vigilance as well as a will to view and treat your chickens as intelligent pets as opposed to stupid, backyard egg-making machines. It also depends on just how much time and energy you're willing to expend on your chickens. Depending on your outlook and how much you're willing to do, maybe it'll be easier just to stew the bad batch and get a new flock, or to give up on the game hens. I have also heard someone say that you can drain an egg and then put hot sauce or cayenne pepper inside, but on the converse, I've also heard that chickens are incapable of tasting hot spice. There's sometimes a "no bite" jelly you can put on a bird that you can obtain from feed stores that discourages other chickens from pecking at a specific chicken that might be over-pecked - the idea being that the chickens don't like the taste of the jelly, and you might be able to put that on or in an egg? Otherwise, I'd say the door knobs ( but NOT light bulbs - if they eat the glass, that can turn out deadly ) and "other junk" idea is also pretty good - the psychology of that is spot-on. They're inquisitive and will peck, peck, peck, but when nothing comes of it, they'll give up... but I wouldn't count on it being as long term of a solution as actively taking a part of their lives and actively setting up and enforcing boundaries.
Anyway, that's my thoughts and my experiences. I hope it helps!