I've tried to use the "imagine you woke up in the body of a [whatever they're not]...." exercise. But it hasn't been effective, because people get interested in imagining how they would feel...and that initial interest trumps the actual result of [what we presume would be] dysphoria. Also, since a frequent response is something other than dysphoria, the analogy doesn't lead them to the point where I want them, rhetorically, to be.
I have had a little better luck with using the current perspective of person I am speaking with to demonstrate the magnitude of their un-awareness. "Doesn't the fact that someone deeply needs to have a very serious surgery - which you cannot comprehend the necessity of - show you how much of a difference there is between a non-transsexual person and a transsexual person?" Often the most dramatic example is MTF SRS. ("She is not a man, which is why you/man are squicked by the idea, and she is not!")
I didn't explain that very well, but it has worked in situations where the other tactic hasn't.