I like @ChicoryBlue's idea of BYC writing something - after all it was educational about the normal behavior of chickens which is something BYC should support.I plan on posting something on the main page warning those who make a living off of YouTube that they could get in trouble for posting things like this.
The lawyers are right about one thing. You have no rights on YouTube. It's their platform. You give up your rights when you sign up. You agree to abide by their decisions.
I think you should explain it to @Nifty-Chicken or one of the mods. I don't know whether it will make a difference but a communication from BYC would be more powerful than just a few of us objecting.
It is right that they have the principle of no animal cruelty - but their algorithm is fundamentally flawed when they allow some of the terrible things they allow and then take your video down. At some level they must sometimes be interested in feedback in order to improve their algorithms.