One problem with your suggestion is that I live in an apartment so I can't make that many holes in the wall.
I was planning on making the lower and upper flat where they join as I only have a power screwdriver and manual tools (not even a real drill).
However, I think I am not going to use the free cabinet doors I got so that it doesn't have to be so tall. I'm estimating that the top of the unit would be around 4' above the toilet maybe even taller and the ceiling height is just 8'. (Note: I'm only 5'4".) So it's back to the drawing board for me.
I will post again on this project, especially if I have any questions.
Thanks so much