Someone on Cigar Weekly gave me some good advice. Don't try and smoke every last bit of tobacco. Keep a little at the bottom that acts as a filter, and just dump it with the ash and dead coals when you're done.
I think trying to smoke every bit, plus the shank in the bowl of my MM Cob were the cause. Now I will be sure not to try and smoke every little bit. Pipe tobaccos are mostly extremely cheap, especially coming from the cigar world, so no reason to worry about dumping a little unburnt tobacco.
I friggin love tobacco!