Clearly what is going on is not any difference in motor performance resulting from the power cord change, but the difference in record magnetization effects.
By using the better power cord, you are reducing the electromagnetic field strength which surrounds it, as seen particularly near the edge of the record (that being the location on the record which is closest to the power cord, and which of course affects the critical opening passages of the music which will disproportionately influence listening impressions for many people).
That reduction, according to my calculations for typical dimensions, is roughly a change from 0.000000000012 newtons per coulomb to 0.000000000009 newtons per coulomb. The reduction in field strength at locations elsewhere on the record is smaller, but still non-zero, being inversely proportional to the square of the distance.
The result is a substantial net reduction in record magnetization, from typically 0.00000000000027 ergs per Gauss-centimeter cubed, to 0.000000000000015 ergs/G-cm^3. A plainly audible difference.
QED!
-- Al :)