Hugh Longworth’s book BR Steam Locomotive Allocations 1948-1968 makes no mention of any Kings being stored/returned to traffic in the period 9/62 to 12/62 but the only Kings to remain in stock after the conclusion of the summer timetable were 6000/5/11/8/25.
There is a photograph of 6011 in use in December 1962 plus several of 6000/5/18.
There is also a picture of 6025 on a race special at Newbury Racecourse station dated 24 November 1962 and 6000 was also present. Did specials that autumn run on more than one day as another picture of 6000 is dated 27 October 1962?