How did these experts account for your house's symptoms? If they "don't know", what are reasonable steps to find out?
My guess is that this non-load-bearing surface is bearing some load.
The amount the wall is compressed in a vertical direction such as to cause a 3/4" deflection in 16'
can be calculated if the shape of the wall is known.
This curve could be a catenary but the engineering toolbox section on load bearing vertical beams may have the equation for this type of curve.
If you think of the wall as a column with an unusual cross section, then, maybe. . .
Or, while the wall is curved, stretch a vertical line and measure the deflection from the vertical at several different points.
Then the compressive distance can be figured graphically. We could be looking for 1/8" or less, vertically, but we need to know the shape of this surface.
If something is pushing out the wall horizontally at the 8' height the curve of the wall will be different than if the wall is being compressed vertically.
I'm wondering if it more depends on the humidity of the inside or outside air, rather than the temperature.
Does the ground freeze in winter at your location?
Do the other walls do it?