I used two strips of cut up credit card to remove my OEM VW Radio from the car, works well
And yes, indeed there is such a small amount of space for wiring behind there, a trick is to tie some string around the bundle, pass it down behind the dash and into the footwell, then you can pull the string as you push the new headunit in, helping to stop the wires just bunching up and giving you no space to click the new one in place in the cage
Also, you may have to swap a couple of wires over, so the new headunit retains memory etc.. as I think the VW loom is not true ISO wiring standard, see
www.installdr.com for pinout
Hope helps
