it is easy to do and it sounds like it is the way to go, the dodgy bit is when its run around the car temporary just to check if it works, you could do it properly without checking first but it could be a lot of work for nothing.
if it flashes with the faceplate off thats a bit more explainable but not, like i thought with the faceplate on and flashing on - off on the random!
have you installed an amp in a car before? because its almost identical to that.
have you looked at the dodgy connections to see if any bare wire is showing or if any of them are disconnected? it does sound like heyho said that the ignition, switch on power wire ( although not run through the ignition for you) may have disconnected but i have never heared the 'cd dragging in noise' coming from a HU with just the constant power connected, so it sounds a bit too dodgy to me, but then all HUs are different i suppose.
i would be happy doing it for you if your not too far away or willing to travel?