It would feel completely awkward, and I would catch myself making all the mistakes that first-timers to that move make, since I hadn't already trained it into muscle memory.

This is an awesome strategy!

One of the things I do to figure out how people can do stuff wrong (i.e. in swimming, which isn't something you can try doing in your non-dominant direction) is to break down the motion into tiny parts and do that tiny part while watching them, to figure out if that tiny part is the one they're getting wrong.

I also do a lot of trial and error, because sometimes someone's stroke will look intuitively wrong to me in a way I can't really explain to myself, so I make a guess, teach them how to correct that, and then watch again and see if my intuition is any happier with it.