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The stone you have may be just fine. You have to find out.
Once you decide it is a good finishing stone you can start introducing naguras.
You can start to use the botan right after bevel set, then...

So you went from 8-10k synthetic to about 3k Botan? That would certainly do it.
Avoid variables when testing!

What do you normally finish on before Escher?
If you can get a good edge on a Thury from ? You should easily get a decent edge from your Jnat.
I am not of the belief that you have to "unlock" a...

So many questions!
Where did you get the Ozuku? Reliable source?, meant for razors?
If you are looking for a Jnat to polish more than synthetic stop looking:)
Hazy is a characteristic of Jnats...