Settings a Cookie by POSTing to a RESTful Magento controller - php

Question

I am building an application which will eventually reside on the same domain where another application resides; both of which are written in PHP. One is a Laravel application and the other a Magento 1.9 store.
To authenticate the user, the Laravel application requires that a certain cookie be set by the Magento store's response, subsequently retrieved and parsed, all before authentication may continue.
My current strategy is a POST to a custom controller which delivers multiple Set-Cookie headers from the Magento store.
The one I need is something like:
Set-Cookie: auth_token=TheValueWeNeedToContinueAuthenticating; domain='.mydomain'; ...
The server I am testing on is an in-house staging environment. The server's VHost is set to Laravel's public directory, as usual.
The Magento store is on a different server however the TLD is the same .mydomain
I have verified the response in Postman, I am indeed returning the cookie with the correct Set-Cookie in place, however it is not visible in my Laravel application as the other cookies from Magento, are. The other cookies were verified within the response as I dumped Guzzle's CookieJar and still received all but the cookie I am looking for.
I am using PHP's Guzzle HTTP Library to post from a Laravel 5.6 app using PHP 7.1
The Magento1.9 store unfortunately uses PHP/5.6.35
When I dump the HTTP response I am getting the cookies which would normally receive had I actually visited any page within the store.
What else could I check to ensure I am taking to right approach to receiving this cookie? Https is the transmission protocol, and the content-type is x-www-form-urlencoded if that will assist an answer in any way.
Thank you.
UPDATE 1.0 - I was able to get a clean error reading from the request being sent.
{"status":"error","message":"invalid request"}
Here is my Guzzle Post request
$jar = new \GuzzleHttp\Cookie\CookieJar;
// Logging my error output -- I can share this if I must
$debug_file = fopen('../storage/logs/debug.txt', 'a');
try {
$payload = 'Knock, knock';
$url = '/api/for/post';
$client = new Client([
'base_uri'=> 'https://mySubdomain.myDomain.com',
'debug' => $debug_file,
'cookies' => $jar,
'headers' => [
'Content-Type' => 'application/x-www-form-urlencoded',
]
]);
$request = new \GuzzleHttp\Psr7\Request('POST', $url, [], $payload);
$rsp = $client->send($request);
dd($rsp->getBody()->read(1024));
$response->getBody()->read(1024) returns the error message