Isn't it fairly obvious what's up? There is a discrepancy between the interpretive implications of the helioseismic observations, and the interpretive implications of the spectral data. Both are complicated affairs, and the discrepency remains to be explained.

Now, I already know how you will respond, because you always respond in the same, predictable vein: Why not assume that the standard model is wrong, and find a better one? But I have a better question: Why assume that the standard model is wrong?

Scientific models which do not sport some discrepency with some observations are actually rather rare, and highly prized when found. So the mere existence of a discrepancy is, by itself, not a big deal. The existence of a lot of discrepancies would be a bigger deal, and maybe a genuine BIG deal, if there are enough of them. But what is really important is the fundamental aspect of the discrepancy, because that is what leads one to have confidence that the discrepancy is of such magnitude as to suggest that the model is entirely wrong, in which case we would look for a better one.

So, does this discrepancy threaten the standard model? it might, one day, but certainly does not now. That's because both the spectroscopic & helioseismic analyses are quite complicated, and there is room for differences due to small mistakes, or systematic bias buried in the data reduction (which is quite different between the two), or some other unforeseen cause.

Now, Bachall et al. had suggested one possibility, that the neon abundance by itself, could be off enough to cause the problem. It turns out that this is most likely not the case. But it is remarkable that such a suggestion would even appear to be right. That diddling the abundance of just one element could, in principle, eliminate the discrepancy altogether suggests that the discrepancy is not a fundamental problem, and will go away (or at least shrink in magnitude), once the kinks in the details of analysis are found & conquered.

So I might ask you the same question now. What's up? Is the standad model really ready for the trash heap now, just because (maybe) the neon abundance is a problem? I wouldn't bet any real money on that.

It suggests to me what it explicitly says, namely that the radius of the sun is not constant, that the sun pulsates slightly on an 11 year cycle. It has long been known that the radius of the sun is not constant, and does vary with time, so that is of little consequence. Fixing the variability to the magnetic field cycle is actually quite encouraging to the standard model, since one would not be surprised by such a coincidence of effects.

Since around 0.995 solar radii, the variation switches from in-phase to anti-phase, it could suggest a "skin deep" effect, but not necessarily that the magnetic field is actually generated so close to the surface. It could also suggest that the field, generated near the tachocline, is subject to turbulent shear, and reconfigures itself (a poloidal -> toroidal transition, perhaps?) near the surface. That would be consistent with the generation of sunspots due to shearing of the field.

Now this observation is one that is predcited by the standard model of sunspot cooling, and is an encouraging observation. The magnetic field of the sunspot blocks convection of heat into the sunspot material, forcing convection to flow around the sunspot, heating the area around it. This is pointed out at the end of the "superficial" page you posted.