Would it work to design the part in the normal attitude, with the machined opening facing up in Z, then just before you post it, swap the letter names of your axis output, ie., switch Z to Y, and Y to Z?
You would have to stay away from using any machine cycles that operate with the 'real' Z axis, as you cannot perform drilling cycles in Y unless you write them out longhand.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)