The factor "Strip thickness affects deflection as the square of the thickness difference ratio" is well-established. J442 allows conversion of, for example, A to C values using a factor of 3.5. Comparing the squares of the mean thicknesses (2.385^2/1.295^2) yields 3.4 - close to 3.5. The topic was analyzed in a TSP article Volume 16, issue 4, 2003 "Relationship between Almen Strip Thickness and Arc Heights". You are correct in terms of the strip's bending resistance being proportion to the cube of the thickness. However the bending moment generated by the induced force in the surface is proportional to strip thickness so the deflection effect is reduced by one power - to two. The predicted effect for the maximum allowed thickness range of A strips is 1.32^2/1.27^2 which equals 1.08 - equivalent to a range of plus and minus 4%.
The depth of the deformed layer is directly proportion to the depth of the indents which in turn is directly proportional to the indent diameter. The volume of the indent is proportional to the fourth power of the indent diameter. Hence the reason for the "fourth root of the hardness ratio" effect. You are correct in saying that the plastic region is much larger than the indent itself. The depth of this region is, however, directly proportional to the indent diameter. Another TSP article "Prediction and Control of Indent Diameter", Volume 18, issue 2, 2004 gives the theoretical analysis.
Just one more comment: your original qualification used strips that were right at the limit of allowed thickness. Perhaps it would be better to select strips near the middle of the allowed range for qualification. Subsequent variations in strip thickness would then have less effect.
