Gini, I had to laugh when you described Magic's "stiff as a board" act...our Valentine (rainbow bridge) did the same thing!!
I think it helps if you leave the carrier out for about two or three weeks PRIOR to the vet visit. The cat(s) gets used to seeing it, even crawls in it so it's sudden appearance doesn't instill apprehension.
I also put an article of my clothing in the carrier so the cat has my scent as a comfort.