Very cool project and good write-up Simon!
Does the setup allow the user to come back to retrieve their quote/info or be able to deliver via a notification email? If not, an answer I wrote on a separate community post related to file retrieval by unique ID might be of interest.
For truly asynchronous request handling, the Gravity Flow Incoming Webhook step type could make some of that handling for future projects simpler. You could keep the same confirmation spinner / result scenario, but only need to be polling the current step while the rest of the API handling is firing in the background.