You are still missing this one: πᾶσα ἡ Ἰουδαία χώρα καὶ οἱ Ἱεροσολυμῖται πάντες. And you are ignoring Mark 1:6.
What does BDAG say about αρχή in John 1:1?
Correct, the second και is internal to a clause and and therefore is not linking two clauses. A clause needs a verb.
The other two και are sequential temporal and do link clauses.
Maybe you should present your case for και. I am so doing something else.