That's a totally different set up than mine. Mine is quite comical , when you see how it works. Next time I remove it I'll post a picture. When you see it , you go "huh".
While your there, will you do something for me? Put it in place , then see if you can reach in where you pulled the radio out , just to see if you can replace the bulb from there. I can do it on mine, I just want to see if that how it's designed for all.