You can DIY this with our article you commented on and our parts. It will be way less than $600 all said and done:
2010 Mini Cooper S Hatchback - Shift Linkage - Page 1. Was this a quote from the dealership? If so, and you do not feel you could DIY this, use this site to find a reputable MINI independent repair shop, which will be way less than dealer pricing as well:
https://www.minirepairshops.com/.