In consideration of this point and the available evidence, I remain deeply unconvinced there is a unrealized, grand philosophical insight to be derived from whatever Gödel’s later, more obscure work had to say about the incompleteness theorems. Likewise Fermat was probably the foremost authority on his most famous conjecture during his life; but the common consensus is that he did not, in fact, have a “truly marvelous proof” of the FLT which he couldn’t fit in the margins.
Everyone thinks silly things from time to time, their prior work notwithstanding. I’m inclined to believe Gödel either wasn’t as invested in the philosophical implications of his earlier work as you believe. Or perhaps he was, but I really doubt he actually arrived at a novel, rigorous result from it. Occam’s Razor suggests we would know if he had.
Aside from that, inability to understand a thing should really count against it. Or do you suppose Miyazaki's Inter-Universal Teichmüller theory is strong because it's borderline incomprehensible?
Like I said, Occam's Razor suggests there really isn't much there.