Yes, WPEngine removed any sign that we could know that is an Nginx server but that’s not problem. You should always see the code if you enter correct address in the addressbar.
I’m pretty sure it’s a plugin (or maybe a theme) conflict. The only way to know is disabling plugins one by one to find the incompatible plugin.
As an alternative, you can also create another WPEngine instance install HMWP with your favorite settings and then use its provided code to configure main website. Note that their settings should be identical.