I have a very similar issue with my 08 535XI 6 speed.with 110K. I took all the steps you did, plugs, coils, checked turbos, vacuum lines, etc. The only code I have is for my HPFP but that's not causing this. I'm 100% sure it's the transfer case. I can tell you that my issue changes with tire pressure. The issue gets way way worse if one tire is low. I still have it with all tires properly inflated but if one is low it gets WAY worse. I'm leaning toward getting either a used one from ebay or you can buy rebuild parts for the ATC300 on ebay as well. There are no sensors in the transfer case to throw a code. The only wires go to the actuator motor, not the transfer case itself.