Flying out early
Flying out early does not seem to be a problem. If it costs more than the flight that CTC would have provided for you then you just pay the difference. The important thing is to let them know as soon as possible if you want to do this as otherwise they may have already booked your tickets.
On a related matter, if you fly via the US then you are allowed a luggage allowance of 46 kilos as opposed to the 20 kg you get via Asia (increased by CTC's negotiation to 30 kg so good on them for that). Might be worth putting in a request to fly that way. (Again you pay the extra if it costs more although when I looked the cheapest tickets were actually via the US.) Also, I know that if you fly Air NZ you only need to travel via the US on one leg of your journey to get the extra allowance, i.e., you can go via the US and return via Asia, or the other way round.