Re: Taigi, Ki, and Time
Not the original poster, and by no means a taigi expert, but....
I'd have to say that you can speed up a taigi several different ways, some of which do not imvolve improving your ki extension. The partners can make their ma'ai shorter; uke can train his abdominal muscles to come up from the mat faster; nage can do the techniques smaller. Of these, probably only the middle one will be okay with the judges....
My experience is that strong connection with partner, so that I feel like I always know where he is, shaves off a couple of seconds per throw and makes the taigi look better rather than worse. Also, strong connection allows you to start the movement of the technique while uke is still approaching, and not just run into him; this shaves seconds too. I'd think of both of these as ki extension.
I'd say that you can achieve the same timing without improving ki extension, but generally at the expense of some other aspect. I train with someone who can "play the Minute Waltz in 45 seconds" but only with a fleet-footed partner with some tolerance for discomfort.... The senior people with more grasp of ki feel much less rushed when hitting the same times.