I've created a new content type called "Form Page", with a required field being a reference to a contact form. So on the page you would have a body, and under that the contact form itself. I can't seem to figure out how to display the form on the page. I either get a link, or the system name of the contact form printed out. How would I go about this?
There needs to be a little more to the Contact Form entity for you to be able to display it. The easiest way to get this is to install the Contact Storage module. After doing this, your manage display options will include "Rendered entity" which will give you the contact form as you hoped and expected!