The mystery deepens!

We have three possible builders: the Woses, the Numenoreans, and the mountain people who took refuge in the Paths when Isildur called, and later became the Shadow Host. Evidence for the Woses: they once populated much more of the White Mountains, and the Pukel-men lining the way to Dunharrow, below the entrance to the Paths of the Dead, were built by the ancestors of the Woses.

Evidence for the Numenoreans: they were great builders, I agree that Ghan-buri-Ghan is saying they "ate stone," and the Stone of Erech reputedly came from Numenor. And it is Isildur's curse that keeps the spirits trapped in the Paths.

Evidence for the mountain men themselves: they make up the Shadow Host, and it was they who took refuge in the Paths when Isildur called on them to go to war against Sauron. There is also the fact that at one time they worshipped Sauron, so it is possible that they built the Paths of the Dead with the black arts they practiced at that time.

I still like the idea that the Woses were the original builders, then the mountain men took over and added their own doors and runes etc., perhaps under the influence of Sauron. But I agree with you that "stone-house men" refers to the men of Gondor and Numenor.

   Morgoth personally was cast into the void beyond the walls of the world, not to return until the end of time. But he had infused so much of his personal power into the fabric of Middle-Earth that the whole place is more or less hot with evil radiation (he was particularly fond of gold, and hence it tends to be a special focus of evil).   I find it very helpful to think of Morgoth's corruption of the earth in terms of radioactivity; there's a little bit of it everywhere (background Morgoth), and it can be concentrated and/or used as a power source.
   Sauron no doubt employs the power of Morgoth routinely, and may have special access to it through Mt Doom (most of Morgoth's power, after all, went deep into the earth). He may have some way to commune with the spirit of Morgoth, although Morgoth is outside the world and technically dead.
   The key thing to understand, though, is that Morgoth was a vastly greater power than Sauron. As Sauron's One Ring radiates temptation and corruption, because it hold the greater part of Sauron's power, so too does the fabric of the earth, the vessel of Morgoth's power, do the same thing; all the world is Morgoth's Ring. This means that we are constantly under assault from evil impulses, and our perceptions are under the Shadow (so, for instance, we may even find fault with the Valar's governance of the world!). In effect, the essence of Morgoth becomes an external cause of what theologians call the Depravity of Man.
   Because of the corruption of all matter, Elves' bodies will not last forever, as intended. This is a problem for their souls, which WILL last forever. Hence, elves in Middle-Earth will eventually 'fade' into something very like a wraith. Apparently the Elven-Rings can hold this effect at bay over a limited area. This is what it means when Elrond says that they have great power to preserve all things unstained - they can exclude the Morgoth-taint, so that places like Rivendell and Lorien give us a glimpse of what Arda Unstained should have been like. The failure of the Elven-Rings after the War of the Ring is why all the Elves who could HAD to sail west; to avoid fading.
   And that should hold you for now.

-- Reverend's explanation of Morgoth's taint. R.I.P., Reverend.