You're right on all counts. We have a great many plans with regard to how we want our network to operate that are underway.
Routed networks tend to fail closed where switched networks tend to fail open. That usually seems to be the problem with layer two failures, they can easily spread traffic everywhere and it takes a while for things to calm down, in the meantime the network hardware is often overwhelmed. With layer three networks the failures tend to be that you lose the ability to route somewhere but in my experience it's often easier to recover from that situation.
I also find it interesting they don't use any additional out-of-band network for heartbeats/management especially as unstable as their layer two network has been. It sounds like file servers need a secondary stable heartbeat network even if it is only 10/100. No judgements being passed here it just seems like a lot of eggs in one basket. That being said, Thank you for this write-up and sharing so openly and honestly. Happy GitHub customer here!
EDIT: Yes, I know routed networks can have similar problems but they are designed for routing, pathing and redundancy with a lot less overhead on the broadcast domain.