Strangely enough, using the SetAngles command just rotates the door but doesn't influence the direction of its movement at all.

I haven't tried parenting the door to another entity ... that sounds very promising though I wonder how this approach will affect the moving direction. I'll try that right now!

EDIT: That did the trick!!! Thanks so much HMW for that tip!!!
Moving direction of the door changes in relation to the parent. YAY ... now I can go back to programming the cube positioner. Shouldn't take too long. Stay tuned.