Sorry to say this, but your theory is wrong.
Tolkien himself says about the Hobbit in letter 257:
Quote:
The Hobbit was not intended to have anything to do with it...It had no necessary connexion with the 'mythology', but naturally became attracted towards this dominant construction in my mind, causing the tale to become larger and more heroic as it proceeded. Even so it could really stand quite apart, except for the references (unnecesssary, though they give an impression of historical depth) to the Fall of Gondolin..and the quarrel of King Thingol, Luthien's father, with the Dwarves.
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~ my emphasis
He himself says that this was only a reference to the, at that time, unfinished story of Thingol and the Dwarves.