Out of curiosity, why are you deploying to all your web servers simultaneously? Could you not do a partial roll-out to make sure something like this doesnt happen?
We have talked about it. It is unlikely to helped with an event like this, and I don't recall an event where it would have. It also has the downside of extending our deployment cycle by a lot. Notably, we do run a canary internally, and that had no issues, which actually through us off for a while because while the app was partially down for users it was working for us and that hasn't happened to us in a while.