You're probably right, but many ordinary get "burned" because they don't call a professional at the first hint of problems. It's unlikely that the bad chimney happened all of a sudden.
I looked for possible causes, but with no reason to connect the
No, everybody doesn't. And they especially don't have all off those things start happening, especially the uncharacteristic headaches. Any time someone start getting bad headaches and/or flu like symptoms and their is combustion close (house or car) one should suspect CO poisoning. That's just a rule, not taught very well though. You had bad luck (or maybe good luck) with changeable weather, but you did suspect something was wrong.
Unfortunately, some professionals don't know much. The first furnace repairman was a dunce, he should have left you with a CO meter, but he apparently was too incompetent do even that.
Your first clue which you ignored was that there wasn't any leaking water but you had high humidity which had to come from some place. The next largest source to a leak would be furnace combustion. CO problems are not common in maintained house appliances. Natural gas is pretty safe, especially with newer appliances. I'm don't mean to jump on you because you missed the correct analysis, since most people probably would. I just objected to the characterization that this was common or a commonly missed problem. Most people that die of CO poisoning do so because they did something stupid or somebody in thier group did something stupid.