The fact that most of the cold start problems occur during moist, damp, days still leads me to rule out a fuel-related problem and focus on the electricals.

I am still thinking that the ignition coil (or coils) is the culprit.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car