OP, get yourself a can of electrical contact cleaner and spray on the mini jack. Then insert (wet) and move around several times. Repeat process 2-3 times. Your minijack contact problems should disappear. BMW uses crap quality jacks to save $1 on your $40K+ car. Same issue on my E90 and at least 4 other E9x cars I've fixed for people.
BTW, the stock system is disappointing even with clean minijack contacts. I sure hope you are satisfied. I had an F30 loaner for 3 days and couldn't wait to get back into my E90 HK car. My inbound F30 will come with HK and I sure hope it sounds every bit as good as the E90 version. If not, I may scream (and find something else to drive).