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This is hard question to answer. It all depends on the hone and the tomonagura, and how prepared the edge is before you get to that stage of the honing.
I typically do two dilutions with tomonagura,...

yes progression, if you stop at 3k you can go botan , mejiro or tenjio.
I find that 6-8k is the optimal starting point for nagura, and I kip the botan.

just mejiro or tenjio then, but you may also need a very good tomonagura, that will depend on the edge you get from the nagura.

What Jnat do you have that you want to use with Nagura?

For me typically I go all the way to 10k then Mejiro then tomonagura on the same base stone.
You can work off your 8k with that method and...

It will take very long time to set bevel with Botan.
The starting slurry is with different coarseness, but I would not call it grit as naturals do not have perfect spherical particles that can be...