Metaphysical systems always grow up around scientific and logical systems and are thus related to them in some ways, but also attempt to transcend those roots to reach a more universal terminus. The problem is that when modern science bumps into traditional metaphysics paradigms are at stake and, secondarily, consensus views of older science are confronting novel interpretations of new science. An important element in this is that in times past the philosophers and the scientists were one and the same people (or groups of people), and when you have that close-knit connection the metaphysics benefits enormously. The article in the OP laments the modern parting of science and philosophy, and this is precisely one of the reasons why the older, unified systems will continue to carry so much weight.
Methodology of metaphysics, or "Metametaphysics" is a tricky field, but it is very unlikely that the entrenched disputes found there can be adjudicated by scientific input. As is so often the case in metaphysics, the causality is rather in the other direction: interpretive debates in the scientific world (e.g. quantum mechanics) depend largely or solely on the metaphysical presuppositions at play. This is why, for many, the methodology of metaphysics is merely descriptive, surveying options, differences, systems, coherence, etc. I would call that approach necessary but insufficient, and yet it does help us understand the primacy of metaphysics over science.