I've never put eggs from another hen under a broody. But, I have had quite a few broodies hatch eggs that were laid by another hen in their tribe.This was a interesting read and I can see many of the points you made. I'm wondering and this is entirely too late but for someone maybe in the future thinking of wanting to add a different breed to their flock that in all likelihood would cause problems similar to Bob's if allowing a broody to hatch out and raise chicks be a better route? Let's pretend that Bob's flock was back to only Lily, Hattie, and Aurora. Let's also pretend that one of the girls went broody, and in order to add Mrs Bob's desired breed he had found and purchased some polish eggs for her to hatch. Would those chicks after they were done being raised by momma possibly have been better accepted into the flock or do you think the original girls would have singled them out after weaning for being so different?
I haven't had a broody hatch eggs from a hen in another tribe.
On the very few occasions a hen from another tribe has tried to lay eggs in another tribes nest the hens attack the intruder. Strangely, the roosters don't and often encourage it.
There is an example of this in this thread.
https://www.backyardchickens.com/threads/cooperative-behavior.1288804/
I would be inclined to believe that any chicks hatched by an existing hen would have a much better chance of being accepted because the hen who hatches the eggs will/should protect the chicks until they are of an age that the broody hen thinks they can cope on their own. This gives the chicks an enormous advantage as one might expect.
If the chicks grow to look radically different from the broody and the others in the group it seems possible that while they may not be driven away they will not have the same status as chicks that look like the rest.