Looks like I figured it out myself.
Had to add the following two lines to the constructor of Bigcommerce.php (The single file version of the API)
curl_setopt( $this->curl, CURLOPT_SSL_VERIFYHOST, 0 );
curl_setopt( $this->curl, CURLOPT_SSL_VERIFYPEER, 0 );
This does present some security issues, but this file will be run locally for a one-off report.