The technician just left, after spending 45 minutes looking the equipment over. What he found was that my furnace exhaust ducting isn't in terribly good condition, so it's leaking a fair bit just as it enters the ceiling of my garage, before entering the wall and heading up to the chimney on the roof.
This happens to be right next to where the return air comes through the floor joists from the second floor. Inspecting that area, he could feel cold airflow which proved that the floor joists weren't very well sealed, and were sucking cold air in from the garage, and since the location of those poor seals happens to be right next to where the furnace exhaust air was leaking, this would explain why I was getting odors in the house. A little bit of gas just as the furnace comes on (a small amount of gas from the fourth burner escaping before it caught flame), and a small but detectable level of carbon monoxide come through the registers (not enough to trip the CO detectors we have on each floor, but enough that his equipment could detect it at the register).
Does that make sense?
So, the furnace is shut down, and his guys will be back out on Monday to repair the leaking ducting, and to seal up the floor joist end (not sure how to describe that any better, sorry).
Now I just need to 1) hope it works, and 2) argue about the $500 labor charge to replace the heat exchanger that, apparently, wasn't the problem. Still, I'm just happy to have found out what's happening, and to know what needs to be done to fix it. I hate phantom problems that are hard to repeat. At least this means it isn't in my head, and I don't need a new furnace.
Thanks again for all of your suggestions and comments - I appreaciate the input greatly.
The good news is the unit is shut down. The bad news is, you are relying on listed CO alarms to protect your lives. Those things are junk. Get the problems fixed then get yourself a low level CO monitor such as CO Experts or NCI
Do you have any pics of this venting? I hope you don't have single walled pipe going through the ceiling.
I hope you know you cannot smell CO. You may be smelling fugitive gas or aldehydes but no CO.
Get those ducts sealed with mastic, balance the ducts, provide makeup air as needed then have them perform a combustion analysis. You have a very dangerous situation there.