Here's summat possibly a bit off the wall - but............

Could it be that the engine smoke is no more than unburnt fuel as the cold engine starts up on rich mode coupled with slightly skanky air conditioning filters giving a nasty smell for a few minutes perhaps?

My wife's E46 has a nasty smell, not unlike antifreeze as the a/c compressor has not been used and mould may have grown on the microfilters. She is now using the full a/c in Auto mode and this smell has become apparent, but only for a couple of minutes after cold start. Once the system warms up it all stops again. It's being serviced in the next week or so and I'm going to suggest she gets new filters.

Just a thought.

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Me:
Current: 2011 E71 40D Vermilion Red/Beige Nappa

Wifey:
Current: 2012 R80 Countryman SDX Green/Cream