Thanks! All good suggestions.
Re: point (4) -- that's actually a bit surprising for us. You shouldn't need to reload your web apps after an outage. We normally restart any misbehaving servers from our side, and if a server is working then it should be a binary working/not-working thing. Reloading the web app doesn't change anything that I can imagine would speed things up again.
That's not to say I have any doubt at all that you really did see your web apps performing badly for the two hours after the outage, and that reloading really did fix it. I just can't think of any way that could happen! More investigations needed...