Looking at the picture of mine peeking out it looks like it's just around the height of the lower edge of the pipes. Looking at a picture of the rear of a Justa it looks like the plastic ends a little below that, seems you could easily put it underneath that. The picture in mini's on-line configuration tool seems to show that location.

As I said it's up to you. the primary reason I didn't do the cooper crap though I look at it is it seemed like it would be super fussy. Here's the process I thought it would take to put my bike rack on:

1) Pop the caps out of the holes in the rear of the mini
2) line up hitch and tighten two bolts to get it installed
3) Put the rack in the hitch, pin, tighten whatever

Here's what I do

1) Slide rack in receiver and tighten bolt to hold it (1upusa.com rack) then snap the safety clip in the eyebolt, and I'm done

I realized I would probably not remove the rack if it took much more work.

 

I have seen your hitch on "S" style bumper: needs cutting... ( do the search on NAM).
Again, have no desire taking off the bumper to mount it. I did that with my Clubman, and when I was trading it in I was too lazy doing the reverse. So, now new owner will enjoy it and I lost $$... It's just me... I read good feed back on Countryman forum about Coopercrap solution so for now I am for that... We'll see by next spring...

I am glad you enjoy yours, of course...