The O-300D mounts are each tubular with a bonded rubber between the
inside tube and the outside tube. They are oriented so that they will
provide radial stiffness but axial compliance, and arranged so that the
engine torsional vibrations are isolated from the airframe. The
characteristics of the elastomer will change with temperature, and the
mounts on the O-300 engines are all on the warm side of the baffling
system.

Usually the O-300D engines are extremely smooth, unless the prop is out
of balance. Maybe your prop has always been out of balance a little,
and the radial stiffness of each mount may be changing enough to create
a resonant system at certain mount temperatures.

Guess two is maybe a mount is bad after all. Next time you have the
cowl off though, try to twist the engine with a long board in the three
axes (vert lateral, and longitudinal) and look at the deformation of
each mount. Maybe one has become unbonded. Don't put more than about
400 ft lbs into the engine block in any axis though.

Guess three is you might also try to spray silicon on the engine
baffling strips wherever they rub on the cowl. In other words, the
transmission path may not be thru the mounts since you have a rigid
cowl.

Guess four is to check the prop balance. I don't think you have a
serious problem but over a long time will tend to crack the cowl and
baffling etc.

The ~ 1 Hz beating (at ~35 Hz I presume?) you describe is weird. Too
bad you can't get a more precise signature or definition using an
accelerometer into the sound input on a laptop computer.