About mokuton I disagree about not being a kkg, here is its definition:
"
Kekkei genkai (血継限界; Literally meaning "a technique limited to inheritance by blood" or "Bloodline Limit") are abilities passed down genetically within specific clans. It's possible for a shinobi to have more than one of these abilities. Kekkei genkai abilities that work via the user's eye are called dōjutsu. Other kekkei genkai include mixing one type of elemental chakra with another, creating a new one unique to the users, which is usually impossible for normal ninja, or other bodily manipulations that are usually unachievable by normal standards"
Besides, I think that here you self-contradicted yourself. At one point you say that that KKG are called also techniques which are created by the mix of other 2 elements because it's considered extremely difficult and yet disprove them, the mokuton, the lava and especially Jinton while the latter is Kekkei Tota.
As for Ashura's reincarnation thing, I have my doubts. Ashura was depicted only once in a fighting scene and that was when he was in cloak. If what you say is correct, then I'm sure that Kishi would have depicted him using it to give a solution once and for all. But no, instead, he prefered to leave it that way. It's just too coincidential to be merely something that happened by luck. Had someone before Hashirama had it, even before Konoha's creation, and had that someone been from senju clan, then it goes without saying that it would have been known, however, no such document exists and everyone regards Mokuton as Hashirama's original technique.
As for the logic of if a jonin can have 2 elements then someone at naruto's level can have 5 again is very relative because no matter how gifted you can be, you need to spend years to get all the elements, take for example Hiruzen, it's not power= more elements but rather how much time are you willing to spend to learn them. Hypothetically, a jonin can learn more of them but maybe they won't be on a good level due to the lack of mastering over them.
What you say about Tsunade and Hiruzen is also very irrational. So on one hand we have a young naruto who, according to you, is fully capable of learning such a powerful technique, which, like sharingan, can also tame the beasts, yet those 2 hokages only care for a mere sharingan? At any point, if they needed a teacher for him, then Tenzo could have done it since he had mastered it but no a hokage with such knowledge over jutsu as Hiruzen didn't even think of it.
And again about KKG, your only proof supposedly of mokuton not being one is that Hashirama learned how to control it but can you show any scans which prove that he didn't get it ex machina, by birth? The definition you gave only covers partially what KKG really is while mixing elements which for normal people is also something almost impossible, can also be considered as such. Based on the latter part of this definition, mokuton is KKG.
For further comfirmation by manga itself check this chapter
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and specifically the 4 following pages, that's a manga fact.
Well Madara can very well know more of it since he managed to gain access to it at the end of the day. Indeed, about Hashirama you're correct, however is there another statement in which mokuton is connected to any other senju? Nope!

Besides, if Kishi wanted to clear the connection between wood style and ashura's reincarnation, then he would have depicted him using it against Indra, not by using his cloak only.