Phantom buster appears to require a manual login before it can get the data, not very helpful if you want to automate the capture of info behind a login.
I have had some success, and some failure, using Linux bash with curl to login and capture the appropriate bearer token… Then make the calls directly for the json data and pass them through to Parabola using php. In essence, creating an API for the data that Parabola can use.
As for your question, if all you need is an authentication cookie, thats easy to grab and with help you may be able to use Google App Engine to host a php script that does it for you. That way you can make the json requests directly instead of parsing through html.