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Could either be the transmission or your mounts. Have you had your transmission drained and refilled? When was the last time you did engine mounts? How many miles are on the vehicle?
The car has 87K on it. The engine mounts were replaced around 60K. I'll have to check when the transmission fluid was replaced. I know that I have replaced it at least once, when my CVT was serviced.
I'm thinking its the transmission. If your lucky a drain and refill will save it. Worst case scenario you will need to decide how much you like your MINI.
Tough shot but it may need a driver save memory reset so the transmission can relearn for a short time and driver habits. It helped me on a little rpm drop kind of like yours but stopped the yo-yo effect from 5-10mph. Made my transmission work alot smoother and better when i did this simple reset.
Resetting the memory for it is in the display panel through the special menu from holding trip button and turning key to position 1, im sure u know? If not can please someone post link?