POW is linked to the event. You cannot re-broadcast the same event with a different POW. The POW relay will have to re-sign it and thus it cannot be a relay since it will have to store the private key. We need a different structure to do this. Maybe a Data Vending Machine.
Discussion
I don't know what DVM's are or how they operate, and at this point I'm too afraid to ask. But I see your point - the note has to include proofwork in the event, and the whole thing is signed. Is it then down to sending the note "draft" to this POW worker, it sends back some kind of nonce/data, and the client then sends off the final event? Amethyst would handle this asynchronously in the background.