I.e. idempotent DELETE with proper protocol behavior requires that one request see the 200 OK or 204 No Content and the other sees 404 Not Found, because the delete has already happened. It would be misleading to say 200 OK to both, because that answer means the resource was there when the request arrived.
Honestly, the whole HTTP resource model has a different conceptual backing for state management than the independently developed "idempotence" concepts in distributed systems. Those non-HTTP concepts came from more message-based rather than resource-based architectural assumptions.
The cleanest mapping in the spirit of HTTP would be that you do multiple round trips. A POST creates a new idempotence context, a bit like "start a transaction". The new URI is the key for coordinating state change and allowing restart/recovery.
As I remember it, the idea of idempotence keys in headers really came from the SOAP RPC mindset. It's kind of funny to see it persisting in some hybrid SOAP + REST mental model.