I'm still interested in a better answer since this solution tinkers with the core installation, but I added the below file to get what I needed, with the following examples:
index.php?option=com_finder&view=search&format=json&q=%22my+searched+phrase%22
index.php?option=com_finder&view=search&format=json&q=my+keywords+to+find
index.php?option=com_finder&view=search&format=json&q=my+keywords+to+find&limit=10
components\com_finder\views\search\view.json.php
<?php
defined('_JEXEC') or die;
/**
* Search json view class for the Finder package.
*/
class FinderViewSearch extends JViewLegacy
{
public function display($tpl = null)
{
// Get the application
$app = JFactory::getApplication();
JHtml::addIncludePath(JPATH_COMPONENT . '/helpers/html');
// Get view data.
$state = $this->get('State');
$query = $this->get('Query');
$results = $this->get('Results');
// Push out the query data.
if (empty($results))
$results = array();
$data['results'] = $results;
$data['explained_html'] = JHtml::_('query.explained', $query);
$data['explained'] = strip_tags($data['explained_html']);
$data['params'] = $state->get('params');
$data['query'] = $this->get('Query');
header('Content-Type: application/json');
$response = new JResponseJson($data, 'Search returned '.count($results).' results' ,false);
echo $response;
$app->close();
}
}