It could be close. I've done mine in June. The dealer charged me $2.6k for the regular service without changing the engine oil as per my request. I just asked them to change the gear box oil instead of engine oil because I wanted to check out the difference of before and after changing the gear box oil which the dealer always claimed as lifelong.
Unbelievable!!! Ur babe's battery has been only used for more than one year, now, it's found 'unservicable'. If so, u can ask BMW for replacement as all Minis ve 2-year-global maintenance. The BMWHK can claim back the parts from BMW HQ if they haven't been consumed in wrong ways.