I am surprised by all the talk of luffing head to wind.
In this scenario, the overlap developed with a clear astern boat overlapping to leeward. Isn't L obligated to not sail above her proper course by rule 17
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If a boat clear astern becomes overlapped within two of her hull lengths to leeward of a boat on the same tack, she shall not sail above her proper course while they remain on the same tack and overlapped within that distance, unless in doing so she promptly sails astern of the other boat.

Is that because her proper course would be to tack?
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Proper Course
A course a boat would sail to finish as soon as possible in the absence of the other boats referred to in the rule using the term.

Because I don't see sailing head to wind as the way to finish as soon as possible. Her proper course takes her head to wind but then is unable to complete the tack because 13 switches on?

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