I switched to dvorak about ten years ago when I incorrectly hypothesized that it might help resolve my wrist pain. [1] It definitely took about a month to get fluid. Once I realized that the new keyboard layout wasn't really helping my problem, I figured I might as well stick with it, since it definitely does involve less wrist movement and such. (I don't know if it will
help with movement stress but it seems unlikely to
hurt. And that's all I've got to go off of, since there isn't really any quality science that I know of in this area.)
But the difficulty of switching all at once is quite significant. I hypothesize that if you used a keyboard editor to switch your keys one at a time, rather than switching the entire layout at once, that you might be able to learn Dvorak while still largely being able to use your keyboard, thus reducing the pain. Given my own subsequent experiments with moving keys around and how fast I can learn single key moves, I hypothesize that it may even be net faster to use this technique than to switch all at once, because I suspect you might be able to do as much as two or three key switches an hour. Possibly even more if you're seriously just sitting there and typing an essay or some documentation or something. What I don't know is what this will do to your qwerty skills. (Though I doubt it will wreck them, but I don't know.)
I hypothesize that learning by switching one key at a time, rather than trying to swallow the entire layout at once, you can learn faster because you get much more rapid feedback when you hit wrong keys than you will from sitting there with a printed chart of keys and pecking them out one by one until you memorize them.
But since I already know a good-enough keyboard layout [2], I have little motivation to try the experiment myself. I'd be interested in hearing about how it goes if someone else tries it.
I further hypothesize that the best first thing to do would be to switch the vowels in under the left hand home row first. So the first move would be to map the O key to the S keyboard key, and thus move the S to the O keyboard key. It won't end up there, of course, but unfortunately since we can only get to the layout by swaps we pass through some intermediate steps that have keys in places they are never mapped. I still think this could go faster than switching cold turkey, though. After that I'd probably go with the right-hand home row, and then expand out from there roughly in frequency order. You may also want to switch both of the [ and ] keys in one shot.
One benefit of the alternate keyboard layouts is that you don't have to "learn" to touch type on a sane keyboard layout. The layout itself rewards you for staying on the home row and you automatically touch type without having to "learn" it. Typing classes would be essentially unnecessary if we used Dvorak on the keycaps instead. The very fact that touch typing is something you must deliberately learn with QWERTY, and apply discipline to maintain in the face of your finger's attempts to do otherwise, in some sense captures in one fell swoop all the issues with using that layout.
[1]: It turns out the correct solution for me for that was to take the keyboard off the desk; I now type with it on my lap, which has solved the problem ever since, possibly combined with an ergonomic-style split keyboard. (Nothing fancy, just the Microsoft split keyboard, not one that is literally in two pieces or anything.)
[2]: By most measurements, you can do better than Dvorak with Colemak or something. However, there's a plateau effect as you get closer to optimal. Having picked Dvorak so long ago, it's not worth to switch to something slightly more optimal. From the perspective of QWERTY, all the better keyboards are better by roughly the same amount. Plus we don't really know what measures to optimize anyhow; we're only making somewhat-informed guesses.