def a rooster
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I also think it a game bantam rooster. I don't see how it could still be laying eggs. It doesn't add up. Just like you said, how can a bird producing testosterone be laying eggs. Maybe I am missing something. I also was wondering why the OP has been losing birds.I still think that is a bantam game rooster of some sort.
But say your vet tech is correct and it's a hormonally imbalanced hen. That can happen when the hen's working ovary (usually the left) is damaged by infection or other cause. When that happens the inactive ovary begins to function, but for some reason it usually produces testosterone instead of estrogen. That causes females to develop male plumage and other sex characteristics though then hen will never become fully male (can't alter those sex chromosomes). As a result hens will stop laying and may begin crowing. So even if your vet is right I don't see how you can get eggs from a testosterone producing bird.
Why have you lost so many birds? Predators?
I agree.Henny feathered game bantam rooster regardless of what your vet says.