Right. You might want to try getting a 'sunlight' sort of bulb - they are kind of expensive but represent true sunlight better than most other lights. Fluorescents can make thing blue/green, while incandescents can make them reddish I think. I've seen lots of artists and tattoo artists using sunlights where seeing actual color, or color matching, is important.
You can try playing around with white cardboard to 'bounce' light from the light source onto your snake indirectly. That will provide light without washing it out too much. Sometimes using a paper towel or other semi-transparent white fabric over a flash will help soften it. There are lots of things you can try, but you want to bounce light onto your subject without necessarily beaming the light directly on it, to avoid glare.
They sell little 'light booths' at Ritz Camera, mainly aimed at auction sellers, it's a little white fabric box, you light it from above and take a picture from the front, the white fabric 'walls' help bounce light onto the back of the item. You could probably rig something similar up with some white fabric.
Generally, bad lighting tends to make a snake look washed out. The only times you normally see an "overly bright" snake, whose colors look way better than they should, is when people mess around too much with brightness/contrast or photoshop. Just with lighting, it's hard to make a snake look "too vibrant". Good, white light and white 'bouncing' material is all you should need. Some cameras allow you to adjust white balance, which helps too - you aim it at a white object near where you will be taking pictures, and it helps tell the camera what "real" white looks like in that environment.