Also seems there's no minification or combining of stylesheets/js and there are query strings on those static assets which is going to discourage caching.
No wonder you need a datacenter to handle that kind of resource punishment!
There are plenty of reasons to stick with Wordpress in a decent sized corporation but if not switching to a static site at least stick W3TC on there so you're minimising your server load and serving out static html and minified/combined resources.
You could then consider using Varnish in front of Apache or maybe nginx with a FastCGI cache.
I"m sure you've got some folks in the team who could whip up a W3TC install in 10 minutes.
Because if it is it from the team that currently can't keep a blog post online when you get a few thousand concurrent visitors, so you might keep yourself open to suggestions and perhaps undertake the BASIC best practices of keeping a Wordpress site up under load.
If nothing else it shows a basic lack of planning for what you know to be a massively popular post, so turn a little of that judgement back on yourselves.
It's possible easily handle tens of millions of hits a day on a tiny VPS if you do even some basics right[1] and that was without any particularly extensive optimisation.
[1] http://reviewsignal.com/blog/2014/06/25/40-million-hits-a-da...
EDIT: I may not be allowed to reply to the comment below due to HackerNews restrictions so incase the option doesn't become available in the next while I'll just say I accept the answer below gracefully, withdraw my daggers and take a calming beer at the end of a long day :-)
I'm wish you continued success and look forward to the next post.
*Edit -> to your above edit -> I think if you expand the comment by hitting the "time submitted" link you can leave a reply, thus subverting HN :P
Yoast is a culprit of performance though.
Don't forget the plugin query monitor and http2 doesn't need bundling resources ( I suppose)