WS Case 118 - "In the definition Mark-Room, the phrase ‘room to sail to the mark’ means space to sail promptly in a seamanlike way to a position close to, and on the required side of, the mark."

While you could argue that P isn't technically required to jibe, she is the give way boat, even though she is entitled to mark room. If P merely bears away to dead downwind (forcing S ti also sail dead downwind) she's still on port tack and subject to rules 10, 14 and 18.2(b) until she clears the finishing line and marks (definition of finish). The best way to avoid a possible rules infringement is to jibe.