Extra holes “sudden death” are considered to be an extension of the existing round, and not a new round. As such, you can’t make any changes before starting the extra holes that you are not allowed to make during the round. The example in the video is correcting a handicap error that was made, but similarly you could not decide to replace one of your 14 clubs with another.
Unless the committee has determined a specific sequence of holes for a play off, you must continue to play the course in order – so if you started at the 10th hole then that 10th hole will be the first extra hole to be played.
Also, as it is a continuation of a round, you must play without “undue delay” – so you can’t stop in the clubhouse for Sunday lunch before proceeding (unless all parties agree to do so and you are not delaying the competition)….