According to my experience:
JSON views: I have created components based FoF automatic JSON rendering https://github.com/akeeba/fof In this way, it is straightforward to load /get queries. In spite of this, certain tasks can simply be solved with a simple Controller function. With FoF, in a perfect case, you can call an Url (index.php?option=com_todo&...
This is most likely because your coffee PHP header() call is conflicting with what Joomla has already set in the framework. Try setting using core Joomla methods:
In addition, have you confirmed the core AJAX functionality is working by testing request on ...
I've got 3 Angular apps running against Joomla right now.
The basic idea is to set up the resource and let it deal with the option/format/controller request fields, then in the controller, call your model to do the math, then depending on where you have stored the result in the model,
$response = new stdClass();
$response->data = $model->data;