I do a lot of macro photography, so I will add a few suggestions.
First, I assume the bug is dead. No live bug will sit still that long. This gives you more choices.
Most macro photographers I know do not use ring flashes. They are good if you simply want to maximize detail, but they don't generally produce pleasing images. They give a very flat light, and they are hard to diffuse.
I doubt very much whether your problem with reflections is because of the color or reflectivity of the interior of your light box. I would bet that it is a result of insufficient diffusion of the light coming out of the box. At close distances, my experience is that one needs a great deal of diffusion. I shoot bugs at lower magnifications than your image--usually about 1:1 to about 1.5:1--but even at those greater distances, I use multiple layers of diffusion for my flash. Also, if your apparatus holds the light far from the subject, it will generate more of an appearance of a spot light.
For live bugs at a magnification of 1.5:1, I usually use this for lighting:
The diffuser body is made of two soda cans, so they are a dull alluminum finish inside. I use the built-in diffuser on the flash and two layers of paper for diffusion at the front of the diffuser. That gives images like this:
You can see that there is still some reflection from shiny areas, but not too much. For bugs with less shiny carapaces, it works better:
For things that don't move, I use continuous halogen lighting. The fixtures (google "hair light") are like the soda cans: the inside is dull aluminum. I tape diffusing paper over the front. I also often add more diffuse light by aiming one light into a reflecting umbrella. I don't have any bugs done that way, but just for illustration, here is a flower:
If you stick with flash and the bug is dead, I don't know why you would need 400 shots on a charge. You could always just put in new batteries partway through the shoot. However, I really doubt you would need 400 images unless you are going to a very high level of magnification.