Seems to me that what might solve some of this e-mail craziness would be to realize better that they are a big company and do more delegation, perhaps to different time zones if they need to have a 24 hour work cycle but more realistically just stop this nonsense and hopefully change the culture to be more logical.
At my company e-mail is something where you expect acknowledgement within 24-48 hours depending on urgency with answers provided on a best availability schedule. Managers also take on fielding a lot of stuff being directed to their reports because they have aggregate knowledge and let's face it distributing a developer for trivial stuff leads to pointless productivity loss.