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 And use a different random key for the copy to yourself, else they can be coorelated.

You don't need to remember any of these keys. 
 Ok, that makes sense. Seems like we could clarify that on NIP-17, unless I missed it. So then the rumor and seal would be identical for both the sender and recipient gift wrapped copies. Just the random signing key and p tag would be different on the gift wrapped copy to yourself as the sender. 
 Ah, never mind. NIP-59 mentions what you just said about sending yourself a copy.

"If a `rumor` is intended for more than one party, or if the author wants to retain an encrypted copy, a single `rumor` may be wrapped and addressed for each recipient individually.”

https://github.com/nostr-protocol/nips/blob/734f379a2a2f225f76f87cdcf074c997a0d40d35/59.md?plain=1#L82-L83