A little additional thought on this, and it's apparent that the 'eddy current' paradigm is misleading. The simplest constraints are of a wire having circular cross-section, but the following argument equally applies to other sections.
For a round wire, the solution is cylindrically symmetric and periodic in the wavelength. Any currents that may flow radially should be periodic at half-wavelength intervals. But skin effect is noticable with frequencies as little as 60 Hz; a half wavelength of about 1.5 million kilometers. I don't know of any power lines that long, so the popular 'eddy current' loops seem misleading. Even at 300 KHz it's shouldn't be often descriptive. The only apparent excuse for perpetuating this phraseology would require a hypothetical inclusion of chaotic behavior of the currents, but this is not included in the quoted formulae for skin effect.
In either case, the cause of increased resistance is the result of induced back-emf.