I wouldn't paint it. While the 4000T might have had a black front, that was not the norm for classic Amigas. I think the current color achieves the proper retro look better.
About the door blocking things, is there any reasonable way to get the DVD drive to push the door open? Kind of like the little doors on many newer cases that push a flap open. I don't know if the drive would have enough force to open that big of a door though.