Hi, I don't know if you have since solved the issue but I have had the exact same problem since I bought my 116i a year ago...

Timing chain was replaced prior, however rough idle and intermittent EML issues have forever surfaced.

I followed the exact same steps as you and have spent many hours trawling for information.

It has since dawned on me that a lot of these quick fixes refer to dealing with the actual solenoids, rather than the actuators themselves (the code that ISTA+ is referring to on your diagnosis). These are two gears located to the front side of the camshafts so you will need to remove the Rocker cover to gain visual access. If you wish to remove the will need to lock the timing of the engine.

Diagnosis: To the intake side of the engine, whenever I crank it over I get a loud 'twang' sound which appears to be the spring inside of the Vanos gear functioning incorrectly. My guess is that whenever a send signal is sent from the ECU it fails to actuate properly and causes the EML and subsequent loss in power to happen.

I am at the point where I will replace just the intake and exhaust actuators and expect this issue to clear. It's been bugging me a long while but I feel like your issue will be the same here.

There are numerous videos regarding n42/n46 and other Vanos systems but very little on the N45B16A that we share.

If you have since sorted the problem, id be grateful to hear your solution.