Thanks again Q!
After posting the photo of my shuttle bay dome I went onto a site with photos taken during the 1991 restoration and found this shot of the disassembled dome:
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Hangar dome by trekriffic, on Flickr
I noticed something right off and that was the insert was made of what appears to be translucent dark green plastic with three rods of red, amber, and yelow projecting up from it at different heights. Of particular interest to me was the dark green plastic. The Polar Lights kit makes no reference to painting the kit insert dark green on it's face yet I think it's critical to giving the lit dome the greenish tint we saw on the screen. Since I've already jammed the insert in so tight it cannot be pried loose from the dome, I've gone ahead and painted the underside dark green being careful not to paint over the other colors. Once it dries I'll do another light test and we'll see how it looks.