I don't understand much from the texts you've quoted
Then that alone should be enough to convince you that there is more to consider here than just input a string in to SHA256 and being happy that whatever it outputs is secure enough to use as your entropy source
Numbers derived from a random number are considered pseudo-random, but they're treated as equivalently cryptographically secure.
What you are talking about here is randomness extraction. This is a whole field of study on its own, and is much more complex than simply "Use SHA256".
Whether you represent the seed with base 2, base 6, base 10, base 16 etc., it doesn't have a difference
Except that you've now introduced a modulo bias.
But damn it Jim! I'm a doctor, not a cryptographer! As I say, I do not know enough about this topic to give you a full technical explanation, and that alone is enough for me to know that I shouldn't be using such methods as my own
ad hoc entropy derivation scheme. Maybe someone more knowledgeable can come along and explain that just taking a SHA256 of some dice rolls is actually perfectly safe, but I doubt it, and until then I'm not willing to gamble the security of my wallets and my coins on an untested method I know I don't fully understand.