Importing the two characters from separate scenes took care of the issue.  Thank you.

It still seems strange to me that I had this issue with them in the same scene, though.  I'm going to continue experimenting more with a single scene file to see if I can figure out what I am doing wrong.  About the only thing I can think of that I haven't tried is the point where you say "select the 2nd character, fire up SkinVue...".  I hadn't tried closing out of the SkinVue window after swapping the first character and then firing it up a 2nd time after selecting the 2nd character.  What I did was:

Fire up SkinVue
Select Mike, click the select button, and then swap
Select Vicky, click the select button, and then swap
Close the SkinVue window.

With importing the characters from separate scenes, I did close down SkinVue in between.  So perhaps that is the key?