I'm so sorry to hear about the deaths in your flock.
I just read the entire post. It seems strange the deaths happen over night. Am I understanding it correctly that every death happened/sudden sickness happened over night? Is there any way a small predator could be accessing your coop during the night?
A couple things came to mind when reading about the first bird with the swelling.
I'm thinking @ Wyorp Rock that you were asking about the tongue specifically in case a poisonous spider/insect stung the hen on the tongue? That would illicit a reaction that would be equal on both sides of the head and neck and possibly tongue....am I close?
I've had lambs experience a severe allergic reaction. Their head became so badly swollen they couldn't lift they're head up. I consulted a vet. (who had sheep.

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His comment to me was if it was a bee or insect sting etc...only the area or one side of the head/neck would be swollen unless the sting/bite happened exactly in the middle of the face. Possible but highly unlikely. His suggestion that the reaction my lambs' had would've occurred from eating a toxic plant in the pasture.
Is it possible that your first hen could have eaten something toxic? Could the consecutive birds have eaten something toxic before night and it resulted in fatality by morning?
Could it be possible that the first bird isn't related to the the other deaths? I've had two completely separate issues happen with my sheep at the same time. Neither ended up being contagious, serious or related. (I hope when I read this in the morning..it makes sense.)