My brother made his old Toyota carola into a manual with a dremil tool and some elbow grease..I really don't know how hard it would be but just getting the clutch peddle installed sounds like a pain in it self..
I'm not the most mechanically inclined but I don't see why it wouldn't be possible? I imagine you will need. Welder for this one preferably a really small guy or gal..lol..
The only thing that makes me question if it's possible is the fact that mini does some very different things in it's line up and the cl*** of car and that it was british and now it's german. And the fact that mini doesn't like to share it's mechanical info with many people,it makes me think you are going to need someone autherized by mini to work on your mini to pull it off? But there are some good mechanics out there..
I would try and push mini to replace it myself if I where in your shoes and I hope they make good it just doesn't seem like your transmission should have gone up on you yet?
And I would recommend the get rag 6-speed! I can't imagine mine with out it...good luck