We can determine the average density of the sun from its size and mass. We can determine its size by simple measurement and trigonometry, and its mass by the gravitational acceleration it produces on everything in the solar system.

From what I understand, Michael claims that our current estimate of the sun's mass may be inaccurate, since we aren't taking into account the possible effects which electromagnetic forces may play. Fair enough. But we have an alternate method of measuring the sun's mass.

According to relativity, light rays passing near a massive object will be bent by its gravity. Photons have no charge, so their paths cannot be bent by electromagnetic forces, only gravity. We can measure the sun's mass accurately, without worrying about interference from possible electromagnetic effects, by measuring how much light from distant stars and radio waves from distant pulsars is bent by the sun's gravity. Measurements of the sun's mass this way agree with the mass determined by gravitational acceleration within 1%.

Therefore, unless Relativity is seriously inaccurate, electromagnetic forces play little to no role in planetary orbits, our estimate of the sun's mass is correct, and the average density of the sun is far too low for any significant part of it to be made of iron. In order to demonstrate the validity of his model, Michael is going to have to disprove Relativity. Good luck!