You absolutely must wait for one request to finish before any other request can return a 409. 409 is a signal to the client that they can stop retrying, the job is done. If some request returns 409 early and the "original" request fails, you will not get further retries and the message will be lost.
Stripe's approach requires serialization as well. Only one request can succeed. If you send multiple conflicting requests in simultaneously, some of those have to block.
The good news is that we have been solving this problem for decades and we have incredibly well refined tools - database transactions and isolation levels - for solving this problem.