I think your problem lies here:
In eemail.php:26-29 you expect the return of eemail::send to be a boolean true, while in reality it is the json-body of the response.
26:$rs = eemail::send($to, $subject, $message, $headers, $attachments);
27: if ($rs !== true) {
28: return eemail::wp_mail_native($to, $subject, $message, $headers, $attachments, $rs);
29: }
In ElasticEmailClient.php:70 you simple return the response-body (which is json):
70: return $response['body'];
The interesting thing is, that in ElasticEmailClient.php:68 you json_decode the response-body, but never use it. So I think you need to fix either ElasticEmailClient.php:70 to look like that:
70: return isset($jsonresponse['success']) ? $jsonresponse['success'] : false;
or in eemail.php eemail::send to json-decode the body and return the success flag as boolean.
I really hope this will be fixed very soon as I just gave you a solution.
Thanks in advance.
David