Here's the
REAR SWAYBAR HOW-TO that I used. I have a few additional comments that might help.
Step 1. I was concerned about jacking since the MINI lacks any alternate jacking points. I made some wood blocks that I place in the channel just forwards of the actual rear jacking point. That way I could jack up the car and still put jack stands under the official jacking points. I'm not a fan if working under a car not resting on the official jacking points.
Step 3. We did not have to touch the ABS or brake lines or the lower strut bolt.
Step 6. Wrestling out the old swaybar: With one person on each side, move the swaybar up and towards the rear so that it is in the gap between the rear subframe mount (right above the angle iron piece captioned "This is the inner bolt location" in Randy's how-to). Rotate the bar 180 so the ends of the bar point forwards. The bar now simply pulls out with minor negotiation around the wheel arch.
Step 8. I had one person sit behind the car and I guided their foot onto the subframe. From this position they could easily push the subframe forwards and hold it while I started all the bolts.
It will take you around 1 hour your first time. Then your ready to motor.