I've had several cases of egg binding in the time I've kept chickens, and none of them presented with an egg that could be felt from the vent. This is likely because most egg binding involves shell-less eggs. And often, two eggs are involved.
At the first suspicion that a hen is having trouble getting an egg out, and sitting in a nest for an hour or more without producing an egg is a sign, I give a calcium citrate tablet whole into the hen's beak to help with contractions to expel the egg. This is the most important part of treating egg-binding. This is the calcium I use.
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