Perhaps your vet isn't familiar with chicken anatomy.  My bet is that they are lodged in the gizzard.
When food is swallowed, it is stored in the crop temporarily while it is moistened and then passes through the esophagus to the proventriculus (true stomach) where stomach acids and digestive enzymes are added. From there it goes to the gizzard (mechanical stomach) where it is ground up. The gizzard is basically a bird's teeth. Small, sharp insoluble stones (grit) are consumed and lodge in the gizzard where the muscles contract and grind up the other ingredients making the nutrients more accessible to the absorption sites along walls of the intestines. Eventually the acidic environment will wear away at the stones and the remnants pass at which time the chickens have to consume more stones to replace their (teeth). Your keys are now grit and they too will eventually pass but not as a whole key.
I have butchered meat chickens that had swallowed nails and broken glass which had become imbedded in the gizzard. No blood was ever evident in the feces. I can't imagine blood being present in your bird's feces. A key just isn't sharp enough to penetrate the tough lining of the gizzard. I think the birds I raise now are much smarter. Part of their terrain was once a dump and they continually turn up glass and metals. I've never found anything like that in their gizzards and I go out every week or two with a bucket and collect any shiny or rusty debris.
There is also no way for the keys to be in the egg. The reproductive tract and the digestive tract are two completely separate systems until they reach the cloaca. By that time, the egg is complete and the shell completely formed in the uterus. You can't push a key into an egg shell at that point.
You may want to review the following information and enlighten your vet about chicken anatomy.
https://www.uspoultry.org/education.../Lesson11/PoultryAnatomyandPhysiologyPres.pdf
I use padlocks on most of my chicken doors. Not to keep people out but for raccoons so I leave a key in each lock whether open or closed.