I suspect some of these older flat earth models, are hiding basic human or planetary truths, veiled in allegory. What better way to hide truths than to dress them up in a flat earth model?
New Earth, you mention Admiral Byrd and his observations when he flew over the South pole. While his observations do seem to loosely support your idea of a flat world beyond Antarctica, it was those same comments of his, that gave the Hollow Earth Society a massive round of applause and boost in numbers. They interpreted his comments to mean Admiral Byrd unwittingly flew his plane into an opening at the South Pole, over the rim, and over uncharted lands of lush vegetation and exotic wildlife, on the Earth's interior.
Again, Sandokhan makes good points about activation of the third eye and spiritual third eye, in viewing parallel universes beyond the astral plane. I've heard the ancients used to stimulate the pineal gland by ingesting gold, to enhance spiritual sight.