The good news is, the model has uploaded in full-color.
Bad news, I broke down and copied by hand the data for each color and re-entered it in Blender Internal. I certainly wouldn't call it a solution, but now I can hopefully move on and order it in full-color plastic, so in any case I'm ecstatic.
A big thanks to all the helpful trouble-shooting from you guys, at least now I know to stay well away from Cycles.
There are a few objects that disappear up when I upload it to shapeways, but the X3D file is correct so if that persists I'll make a separate post for it.
Last edited: Aug 22, 2014