Disclaimer: I am not a doctor. I am not an expert on the anatomy of the hand. I am only relating my personal experience. With that said...
I must strongly disagree that moving as little as possible gets you CTS. The hand is an incredibly complex part of the anatomy, and it didn't evolve in order to allow us to type. Therefore, any thing that resembles typing (computer typing, playing the piano, guitar, violin, etc.) must be considered an unnatural activity. Not that people shouldn't do these things, but that they should be careful when they do.
Conventional wisdom, especially in the area of playing musical instruments, suggests that in order to avoid CTS, the hands should stay as relaxed as possible when doing one of these activities. I don't know what research in this area has revealed (if anything), but I do know that staying relaxed has worked for me, both in typing and in playing the piano, and it has worked for countless other musicians.
As far as Dvorak is concerned, current computer keyboards require you to contort your hands no matter what layout you're using, whenever you have to reach for keys. The hand cannot be relaxed when it's contorted. I've found that Dvorak has moved the less used keys to those contorting areas, so you contort your hands less. Therefore, I agree with the original poster that Dvorak feels better.
I did a little googling on the Reach Method you talked about, and it looks interesting. I'd like to point too though, that it could be used equally well (if not better) with the Dvorak layout.