Element API + JSON data in template
I can't think of a clean way to do this.

The Element API plugin currently will set JSON headers on the response and return the data JSON encoded, so it's not easy to directly embed in a template.

A few options I can think of would be to fork the plugin and add the ability to return JSON in the format a template can directly utilize.  Or you could have a wrapper plugin that made an AJAX call to the Element API endpoint, grabbed the response and massaged the data into a format your template could directly utilize.