I know Jacques didn't mention that the problem was with the stock installed-with-Wordpress Recent Comments widget until a couple of hour after you posted that comment, but _surely_ someone at WPEngine knew already that this wasn't a "custom code" issue?
From what I'm reading (and please correct me if this is wrong) a stock WP install with no plugins or custom themes, but with several hundred thousand rows in the comments table and the Recent Comments widget running - will crash hard on WPEngine (while running just fine on a "loltastically over provisioned Linode VPS).
In my view - that's a "Wordpress support issue" suitible for diagnosis by a "Wordpress expert", and a long way from "consultancy" for "building custom code".
It's true there needs to be a limit to what customers expect from hosting companies, but like it or not, you've set the expectation bar _very_ high with the marketing copy on your homepage, and you've got a wonderful social media reputation based on those expectations. At some stage, you need to suck it up and dedicate the time/expense to live up to that reputation, or inevitably social media will bring your reputation back down in line with your business behaviour/policies - and the wider the gap between the expectations you've set and the service you deliver, the more ammunition you're handing over to "the haters" to shoot you with.