I was thinking to use a Naniwa Super 3K after the 1K (instead of using the slate with water) do you think it could be useful?
Yes, the finer you get the bevel stria and edge straight the easier it is to finish on a Jnat.
But most Jnats should be able to remove 1k stria with Diamond slurry. I often go to a Jnat, from a near mirror 8k. That way all the stria is Jnat and the edge is already super straight. The Jnat is just a finisher and I quickly get a Kasumi, hazy finish, and very straight edge.
Diamond slurry works well to remove deep bevel set stria, but because it is removing a lot of metal that stria will be contaminated and will not break down as fine as clean fresh slurry.
So, you can make diamond slurry and remove the deep stria, then wash the stone and razor and make a new diamond slurry and break that slurry down to fine polishing slurry.
I use circles to remove deep stria or to work a slurry to break it down faster. Circles are more aggressive for removing metal because you are attacking the steel from multiple angles in stead of just a back-and-forth motion.
You can work Diamond slurry very thin but, it is just the grit from the base stone. If you use a Tomo slurry, you are using the base stone and the Tomo grit. If the tomo is finer you may get a finer slurry. But if the Tomo is courser or does not break down at the same rate as the base, it will be a courser slurry. You just have to experiment.
It is not as simple as that, because there are other factors, pressure, technique, how much slurry you start with and how you thin the slurry for a few, and the razor steel, but it is a good start.
Another trick to try, when you are thinning your slurry is to remove some slurry from the stone, scoop it up with the razor, then with a finger squeegee it off into a container, I use ceramic soy sauce dishes. So later if you need more clean slurry you can add slurry that is already broken down to the stone it needed.
Experiment with both techniques, 1k Diamond slurry and 1k, synthetic pre polish and Jnat finish. Document your results with micrograph photos and test shave and see what works best for the razors you have.
The steel of your razors also plays a part in which method works best for the razor. Develop your own bag of tricks.
The good thing is you are honing all the way to the edge, getting fully set bevel and nice even stria patterns at each stage. That is the hardest thing for new honers to grasp. You cannot refine an edge that does not exist.