g_wilson, I attempted to follow your directions, but failed due to noobness. I got a bit lost there, especially in the "select instances" step (could not find that in any menu/pop-up menu?). I did mess around with components, but getting Sketchup 2014 to transfer changes from one component member to all of them . . . didn't work. Selecting them all and scaling them all simultaneously brought about the usual behavior (centers of circles moving around). So, I solved my problem by starting from scratch and using circles of the needed size instead of scaling anything I had derived from another model.

SketchUp will baulk at making an edge < 1/1000th inch. It will consider the two points that are needed to make it to be coincident ! 0.5mm is about the limit. 1mm is safer. Any operations like a Circle or FollowMe etc which try to create very tiny edges will fail because of this 'limit'. Hence the Scale up 'trick'... These kinds of tiny edges can exist [e.g. when you Scale down afterwards] - but they cannot be created.