Thank you all for your great suggestions. In particular, although I did examine the bead area very well (with the tire on its side so that that area was completely covered with soap solution), I did not pay
that much attention to the side walls and I might have missed a pin-hole leak in that area.
As a next step, I've gotten my wife's permission to fill our bathtub with enough water to completely submerge the bottom portion of the upright tire/wheel, but not so much that it will "float" the tire. After waiting for a few minutes for the water to completely "quiet", I'll check for leaks (tilting the tire a bit to examine the sidewalls) and then, if necessary, rotate the tire so that a new portion is submerged. Etc.
I'll start off with the valve completely submerged, then the plug, then to the rest of the tire/wheel.
Luckily, I already washed the tire and rim very well yesterday, so it's not going to dirty the tub appreciably.
I have only one question at this point. What is the absolute maximum pressure to which this OEM Potenza tire can be inflated? The sidewall states "never inflate above 40 psi", but I believe this is advice about operating pressure, under load, at speed, hot, etc. This will be "just sitting there", and I want to find the leak, but I don't want to have the thing explode in the tub.
I'll report back what I find on this Reality TV nail-biter.
Thanks again.
Edit: What is the fix, if any, for a true pin-hole (not nail-hole) in the sidewall -- Green Slime time?