| Done it, not a nice job but very doable. A LOT easier in a proper shop with a lift and a tranny jack. I did it in my garage, jackstands and an engine lift.
Anyways, pulling the tranny out is straightforward, splitting it to install the LSD is a snap.
You will trash the thrust bearings on the old spool trying to pry them out so you will need a pair of those. MINI does NOT sell the bearings so you have to source them yourself, using the numbers stamped on the races. As it is not a hypoid gear set, no need to preload or anything like that. In go the new bearings, you drop the spool in its place, button the sucker up and you are set. A friend will come in VERY handy if you do not have a tranny jack.
Hope this helps | 
