The result is so that the flux is more concentrated near the surface and it is minimum on the axis of the cylinder.

This effect is described in Sylvanus P Thompson's 1901 textbook "Dynamo Electric Machinery" but without your mathematical analysis.
He placed coils at various depths inside an iron bar of substantial diameter to measure progression of flux from periphery toward center. His interest was railway dynamo poles.
It was a problem in control rod position indication for some early nuclear power reactors.
Eddy currents changed with temperature and affected indication, which was based on flux.
There's still some investigation to be done on that system.
Would your formula from post #11 lend itself to calculating flux in a ferritic stainless steel cylinder placed inside a solenoid with AC excitation?
Perhaps you know of a reference book.
thanks,
old jim