Probably too late to matter, but...
Cross-polarization is often effective in these circumstances, meaning that you mount linear polarizers to your light source[s], and then use a circular polarizer on the camera, oriented at 90 degrees to the ones on the light sources. If you do it right that will eliminate basically all specular reflections.
Another option is tenting, in which you surround the subject with a white fabric tent, and then shine your lights on that from the outside. The idea is to make the light source very very diffuse.