The fractional percentage camp is based off the observed spectrum. the most of it camp is based off observed material composition in the solar system.
Here is the stellar remnant theory. I found it a bit extreme, but fun to think about.
https://arxiv.org/ftp/astro-ph/papers/0410/0410569.pdf
Personally I would bet on the sun(as it is a second generation star)having a more substantial iron core than first thought, probably a quarter of the mass, too much iron, there would be no fusion, but it does not make any sense to me that as full of iron as the inner solar system is there would be negligible amounts in the center of the sun. Perhaps there is an unknown mechanism that prevents the iron from creating photons to sus out with spectrography(my guess is the thousands of kilometers of hydrogen around the core).