The starting point is understanding when boats in this situation are overlapped.
See Definitions Clear Astern and Clear Ahead; Overlap
Clear Astern and Clear Ahead; Overlap One boat is clear astern of another when her hull and equipment in normal position are behind a line abeam from the aftermost point of the other boat’s hull and equipment in normal position. The other boat is clear ahead. They overlap when neither is clear astern. However, they also overlap when a boat between them overlaps both. These terms always apply to boats on the same tack. They do not apply to boats on opposite tacks unless rule 18 applies or both boats are sailing more than ninety degrees from the true wind.
So, as is usually the case with boats approaching a leeward mark on opposite tacks, both boats are sailing more than ninety degrees from the true wind, the definition of overlapped applies and they will probably be overlapped. Whether boats are overlapped, clear ahead or clear astern, when the first of them reaches the zone is what determines the entitlement to mark-room. So, looking at the diagram
@1 and @2, both boats are sailing below 90 degrees to the true wind, neither is clear astern of the other, so they are overlapped.
@3 boats are still overlapped: B is not clear astern of the line drawn through Y's transom.
@4, Y is clear ahead of B.
@5, Y and B are once again overlapped.
So, applying rule 18.2( b ).
If Y reaches the zone @3 (Zone Boundary #1 in the diagram), then she has reached the zone overlapped inside B, and is entitled to mark-room, and any future gybes or changes in clear ahead/astern or overlap will not affect this entitlement.
If Y reaches the zone @4 (Zone Boundary #2 in the diagram), then she she has reached the zone clear ahead of B and again is entitled to, and retains mark-room.
If Y reaches the zone @5, she reaches the zone first, overlapped to leeward outside B, and B, as inside boat is entitled to mark-room, and as before any future gybes or changes in clear ahead/astern or overlap will not affect this entitlement.
So to answer your specific questions.
1. If the other boat gybed within 3 lengths of the leeward mark do I have any rights?
The issue is not whether the other boat gybed in the zone, but whether or not she reached the zone clear ahead or overlapped inside you, but if the other boat gybes in the zone, probably the situation illustrated by either Zone Boundary 1 or 2 above applied and you would be required to give the other boat mark-room.
2. If the other boat has not yet made 3 lengths when I become overlapped on him do I have rights?
If the other boat gybed outside the zone and you were overlapped inside her when the first boat reached the zone, then you were entitled to mark-room.
3. How does the benefit of the doubt work here? Due to the angles we were sailing the other boat only became closest to the buoy just before I rounded behind it.
I think once you understand about boats on opposite tacks being overlapped, there's not much doubt about the issue of which is inside boat.
The test if NOT 'which boat is closest to the mark'. Consider two boats approaching a gybe mark on a beam reach, with the trailing boat only just overlapped bow to stern to leeward of the leading boat when the leading boat reaches the zone: leeward is quite a distance further from the mark than windward, but she is clearly the inside boat.
It can probably be said, for boats, overlapped approaching a leeward mark, if the mark is to be rounded to port, the boat on the other boat's port side will be the inside boat and vice versa for a starboard mark.
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