Field Collections not displaying in Content Template
Not necessarily an answer, but a viable workaround: 

The Field Collection content is available to views, so I made a view block that prints out the Field Collection content where the contextual relationship is the node's NID. That block gets displayed on this content type only. With some Javascript trickery, I'll be able to position it where it needs to go. 

I'm open to a real answer, but for now, this is all I've got.