Another thing to consider: mold/mildew in the holes around the top of
the bowl...and in the over-flow / vent hole in your sink.

I've been chasing a similar problem in an under-used bedroom bathroom
for a few months now. After what seemed like countless hours playing
"Columbo", I traced the origin of the smell to this mildew build-up.
The problem is - cleaning it isn't easy. I've been flushing both
areas with bleach off and on. The smell goes away (as does the
"visible" mildew)...but comes back eventually, as the mildew grows
back. It's hard to deeply-clean these areas, because there is no easy
access to them.

I realize that I could just solve the problem by replacing the sink
and the toilet, but that seems like a waste; There's nothing
mechanically wrong with these units.

Just my two cents.