At last, at last, I can breathe again.
There was a secret open drain to nothing inside the wall behind the furnace, branching off from the sewer line coming down from the kitchen, venting up rotten gasses from the depths of hell right into the air return path.
No idea what could have been down in the furnace room once up on a time to make use of that drain. Not sure why it was just walled off instead of closed when the furnace was installed in front of it. Hard to say why it would have taken this long for the trap to dry up. But shame and frowns and shaken fists upon whoever decided that HIDING AN OPEN SEWER LINE INSIDE A WALL USED AS AN AIR INTAKE WAS A REMOTELY O.K. THING TO DO.
Anyway, after ripping open the wall, capping off that pipe, and venting out the house once more, I can sleep in a room that is both cooler than 88° and does not smell of death, which, let me tell you, is pretty swell.