The climate control unit as catches on its short sides. Removing the radio won't assist you but taking out the clock and switch panels may. The clock and switch panels have catches on the upper and lower edges and can be removed by inserting cards/sheets there.
I've got some photos somewhere that I'll send so that you can work something out.
I've also got one of those bulbs out - but I can't remember if they're accessible or even replaceable!