Dave,

If you have attic space I'd go up there and look around.
Something may be too close to your chimney or stove pipe.

Nope, no attic. We have vaulted ceilings. I boxed in the chimney pipe where
it passes through the 2x12 rafter bays (with about 3" of air space between
the pipe and wood). It's capped by flashing on top and a trim ring on the
bottom. Nothing can get in there.

In addition, the smell is noticeable long before the chimney pipe is even
warm to the touch.

Are you sure about the trash?
There's a lot of plastic in junk mail.

Nope, I never burn paper, junk mail, or any other kind of trash. Only dry
wood (Logs, woodworking cutoffs, NO pressure treated, NO plywood). I use a
couple of "fatwood" sticks to start the fires.

Anthony