Simple solution:
If you are not attacking other ships, nor raiding the land from the sea,  you are neither pirates or privateers, simply the crew of an armed merchant ship, and the terror of pirates, who hate ships that can fight back.
An armed merchantman that obtains a Letter of Marque becomes a privateer.
Note that a Letter of Marque does not need to come from the King, or even the Kingdom, which addresses the 6 month problem.
A Letter of Marque from the Kingdom Seneschal would be perfectly valid at a Kingdom level, or one from a Baron or Baronial Seneschal would permit you to style yourself  "Privateer of the Barony of XXX".

Such a Letter, once obtained, would be valid as long as a State of  War existed, (continuing to prey on ships when no state of war exists is piracy, even if a Letter of Marque is in your possession) and there would be no need to obtain a new one from each reign in person.  That's what the Post is for, to transmit legal documents as needed.

David Gallowglass