My method for 14.73 isn't worth it by the full game clock at all. It might even be system- and mission-exclusive.
For starters, note that the zone that triggers the missile launch countdown is a roughly cube-shaped area encompassing the square perimeter, and reaching from the water surface to a peak just below the top of the tier-2 walkways. What I do is make sure I'm in hard mode with a Dreamcast, then grab the missile once normally, and put on the board
(as I'm sure you're familiar with). This misses the shaft completely, and lets me fall--aim for the upper half of the right side relative to the camera, but do so at such an angle that you miss tier 3 and land on tier 2. If you don't fall off, slide over into the corner, and since it's hard mode there's an enemy here that shoots you, conveniently making you lose the board. Alternately, if you don't put on the board, the Dreamcast fall angle (again, apparently only in hard mode) gets you stuck on an interior lip of the shaft; superbounce out and you don't need to worry about getting hit or having to land with space-shuttle-like precision.
Anyway, since the polyhedron to start the missile timer doesn't trigger until just below tier 2, you're here with no missile timer. The missile is not grabbable until the timer starts, so you need to do that. Fortunately, here's what you can do: jump past the spring, hopefully squeezing between the small gap between it and the missile. Turn around in midair to face the other way, and when you think you're just a bit below it, do a homing attack to reach up and hit it. With any luck, this homing attack will come just after you touch the top of the missile trigger, and you'll grab it in 14.6 or better.
This becomes non-version/mission exclusive if it's possible to super bounce from the opening section of walkway, landing on tier 2, but I've found so far that there doesn't seem to be enough room to do so until the spot you use at the octagonal platform, which also starts the timer.
