When you pulled the plugs, was there any oil in the plug tube shafts (plug holes in cam cover)?

One of the first approaches to miss fire/stumbling, is to do a quick process of elimination. Hand on tail pipe- is there a DEAD miss or random cyl drop off?
Ignition side- all OK plugs coils, etc
Fuel side - what is the pressure in the fuel rails? Do the injectors misfire, drip, spray patterns equal cyl to cyl?
Air intake - filter to cyl head. Clean, sealed, and not deteriorated?
Oil Separator - leaking, split, puking oil everywhere? (Mayo under oil filler cap?

Misfire can be read with a scanner. Move around cyl to cyl or stays in one cyl?
Stays- look into THAT cyl - Ign & Fuel delivery systems
Moves- look up stream - Ign & Fuel delivery systems and look for AIR LEAKS. Your smoke detection method shows a leak in the intake area at the DISA valve. Pull and inspect.

This list of test and measure has been around since the '60's..... The only changes is what happens upstream to the fuel (injected vs Carb) and Ign (coil on plug vs cap/rotor/wire) systems.

Helpful?

__________________

2005 X5 4.8IS
The Blue ones are always FASTER....

Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green