We have a couple of issues at play here.
I don't know if this is feasible since I'm not sure how things look like in your facility, but could you come really close to the Lexan plastic with your lens, and still take a photo of the machine? By placing your lens as close to the glass as possible, you will negate almost any of the glare that would be reflecting off the Lexan. You could also experiment with using either your hand, or possibly a lens hood, to shade your lens from the Lexan reflections (if you can't bring the lens close enough to the Lexan).
The alternative would be to either set up a machine sans Lexan specifically for the photo shoot, or to kill the overhead lights and take super-long exposures. Unfortunately none of these "solutions" are terribly easy.
The dull green fluorescent lights
Aside from making a case with The Boss to change that dull green malaise to something more worker-friendly, I'd recommend creating a "Preset" white balance setting on your camera. That setting will tell the camera what "white" is supposed to be under your lighting conditions, thus adjusting the white balance properly.
I'm not sure which camera you use, but here are the instructions for creating a preset white balance setting on a Nikon D7000.
Hope that helps!