I have heard a couple of the guys have BST issues like you described (not 100% same) but I have also found that with a good battery many e53's with similar issues had connection problems with the B+ or the ignition switch.

Sent from my SM-A730F using Tapatalk

__________________
"When the Team Chief said.... You're trapped in a hole with nothing but a goat and a slinky, what do you do? Stubby said, I'm not sure but it won't end well for the goat...." ~(Overheard) Last day, Phase 3, Q Course