I'm on port and closer to the windward mark — don't I get mark-room?

No. Rule 18.1 switches Rule 18 off between boats on opposite tacks on a beat to windward. With no mark-room in play, plain Rule 10 decides it: the port-tack boat must keep clear of the starboard-tack boat. Being nearer the mark changes nothing — duck or tack. “I'm at the mark, so I have rights” is exactly the myth that causes windward-mark pile-ups.

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Next on this shelf — The Windward Mark