The trick is to make the background consist one background plate (as you have done) and add the shiny glass as new layers on top of it (two different, since you have two shiny glass effects). To accomplish this - duplicate the background and alter it's shape so it gets the shiny shape 1 and add it on top of the background. Repeat and create the second shiny part.
You'll get the darker edges by applying an inner shadow (settings shown as picture 1A).
1A. Settings for background
- shiny 1
The lighter borders has been done by changing from a dark inner shadow to a light.
- shiny 2
Get the AI file here.