Need advice on recently purchased 2004 4.4i X5

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I recently purchased a 2004 X5 that is in relatively good shape mechanically and physically. I did my due diligence and researched the vehicle by obtaining maintenance history, car fax info, test drove the vehicle twice for extended periods and mechanical inspection. All was well until I brought the vehicle in for service at my local BMW dealership three weeks ago. The dealership was/is running a special on some of their routine maintenance which I decided to take advantage of as a form of preventative maintenance. I authorized them to do an oil change, fuel system cleaning (which includes high pressure injector cleaning, new fuel filter and air filter) and brake fluid flush. Upon picking up my vehicle, I instantaneously notice something was not quite right. At idle the vehicle would vibrate heavily and when attempting to pull off in first gear the vehicle would briefly shuddering. Thinking this would be a quick fix as the issue is mostly likely related to the work performed, much to my dissatisfaction I am now three weeks into this ordeal with no answers as to the root cause of problem.

Initially I was told that the problem is a random misfiring occurring in different cylinders that is probably related to levelers within the engine. They've changed the levelers but the problem still persists. They've changed the DME, the fuel filter again, the fuel pump, the MAF, the air filter, fuel injectors, the gasoline and I am told the problem still persist. Now I am told that the issue is "no misfiring" but rather they suspect that the flywheel bolt between the engine and the transmission could be loose. To say that I am frustrated by this situation would be an understatement. The vehicle had no such issue prior to the work done some I am not buying the flywheel bolt line.

At this point I have no choice but to let them continue investigating which initially the shop manager indicated will be on their dime (although no one has said anything contrary to the manager, I can’t help but feel that they will find a way to stick it to me in the end, i.e. flywheel bolt). Each passing day the diagnosis gets more and more invasive with no results and at this rate I suspect they will soon tell me that it is something within the transmission.

Has anyone here experienced the heavy vibration at idle and shudder when pulling off from first gear before? If so what was the root cause? Does the flywheel bolt theory that the dealer is now suspecting even sound plausible? I personally think the explanation for this issue is possibly far simpler than what’s being tried and is most likely related to the work done on the vehicle.

Thanks in advance for listening and for any advice.