Can the outside starboard-tack boat refuse mark-room to an inside port-tack boat?

No. Once boats are clearly overlapped when the first of them reaches the zone, Rule 18.2 requires the outside boat to give the inside boat mark-room — and at this mark it does not matter that the outside boat is on starboard and the inside boat on port. The overlap at the zone is the snapshot that decides it.

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Next on this shelf — The Leeward Mark