For the past few years I've considered learning the Colemak or Dvorak layout, but the biggest hurdle is my muscle memory for Emacs. I'm sure the same can be said for any (heathen) Vim users, too.

It seems kind of dumb to rebind the keys so that the positions of commands don't move on a new layout, especially since many have mnemonic meanings. Does anybody have experience, good or bad, making that switch?

Good luck with switching if that's what you choose to do.  I gave it some thought a while back, but I already type 120wpm and just don't feel the benefits would be worth it (to me anyway) to justify torturing myself with trying to supress 15 years of muscle memory.  Kids today should not be learning qwerty, but I think my generation is hopelessly stuck with it. 

but the biggest hurdle is my muscle memory for Emacs

I've got quite a particular Emacs setup because I find the default Emacs keybindings to be the madest shortcuts ever invented ; )

Two examples: the "C-x ..." and "M-x ..." (on a QWERTY keyboard) are just plain ridiculous and C-n C-f C-b C-p to "move the cursor" are totally crazy too.

And the entire Emacs keybindings are crazy like that.  I mean... Quite some people are considering Emacs to be responsible for some forms of RSI like the dreaded Emacs pinky syndrome. That is terrible in my book.

But then Emacs is entirely configurable: so I did remap basically everything.

For example I did remap ctl-x-map to "CTRL + one key that is easy to reach with the right hand".  I'm hitting CTRL where it should be (CAPS LOCK on some keyboard, that I remapped to CTRL), using the left pinky and then I do "C-x" using, say, "C-," on a QWERTY keyboard.

If I were to switch layout, I'd still use the same fingers: I only care about the physical position of the key.

Same for "moving the cursor": I use an "inverted T arrow" located on my right hand's home row.  On my QWERTY keyboard that could be: "alt+{i,j,k,l}.  I'm using ALT instead of CTRL because I'm hitting alt with my left thumb.  So, say, ctrl+p (two pinkies, ouch Emacs pinky) becomes alt+i (less fingers movement, stronger fingers and... zero pinkies involved).

Should I switch layout, I'd remap my Emacs and still use the same fingers / physical key position.

I'm not saying that you should replace all your shortcuts with shortcuts easier to touch-type or less pinky-problems/wrist-problems inducing: a lot of the mnemonics are actually quite useful, especially for the ones you don't perform all the time.  But honestly to move the cursor around I'm not thinking in terms of: "'f' means forward, let's hit 'ctrl+f' and that shall move the cursor to the right".

I'm also totally convinced that spending the five minutes it takes to install and learn ace-jump-mode saves a lot of keystrokes (using the last version of ace-jump-mode you can "jump" besides any buffer / window).