"RE: Ken - can you shed some more light on what the advantages of the "natural stone sharpening" are? I'd definitely be willing to invest if it makes sense for these types of knives ... perhaps $200-$250 for a good set of stones."
I mention natural stones in that I really like them used on carbon steel knives. Of course not everyone will feel the same way about this and I certainly don't want to give the impression that I've stopped using synthetics either.
So let's divide the topic in half - aesthetics (looks) and performance.
Some like blondes, some brunettes, etc. Synthetic stones, with some exceptions will give you a shiny finish - a bright mirror finish. It will treat the softer cladding of your takeda the same as the harder core steel - the aogami super - the same way. You get a bright finish. This is attractive in it's own way. A natural stone will treat the two steel components of your knife differently, contrasting the two. Having achieved this finish, you will begin to appreciate subtle aspects in the steel that get brought out. You will develop the sense of appreciation that sword polishers have in that they are optimizing or bringing out the work of the bladesmith in an optimal manner, displaying the subtle characteristics of the blade. This is true for clad blades and differentially hardened blades. Here the separation in a differentially hardened blade is marked by a line of demarcation between the two - a hamon line. If you look closely at the line, you will appreciate interesting detail - niori, showing various structures that modern metallurgists recognize as martensitic and pearlitic structures formed during the tempering process. It is not unlike what metallurgists view in their prepared specimens. This is part of the art of the swordsmith revealed by the sword polisher. With synthetic abrasives it is all a whiteout - just a shiny surface with no detail - similar in photography to an overexposed picture. Admittedly this high contrast is an acquired taste and even among sword polishers of various schools of thought over various periods of time, the degree of contrast considered optimal varies and there are 'arguments' about this topic. Various natural stones will provide varying levels of contrast. At some point after sharpening many knives, you will wish to go beyond 'merely' sharp and begin to consider the beauty of the knife as a part of your task of optimizing your knife. Now the fun begins as you go from house painter to portrait painter
You will modulate the contrast. You will look at the core steel mirror finish and see that the natural stone finish will impart a subtle black haze like an antique mirror - a kurobakari finish.
As an example, I recently worked on a Tojiro white steel petty. The original finish had a sandblasted high contrast finish. Very fake looking, but most won't notice it. Very uniform. I redid it with natural stones. A completely different look, revealing an uneven bevel and a false line of demarcation between the cladding and core steel (jigane and hagane, respectively). It took more work to even out the bevel which was masked by the fake sand blast look, but it revealed a beauty hidden under the original finish. This is not something you can accomplish with almost all synthetic stones (some Nubatamas being a notable exception). Personally bringing this level of beauty and uniqueness in the blade 'out' for viewing is more interesting to me than a beautiful handle. Of course both is even better. You tend to find that just a bright mirror over the whole edge seems like looking at an overexposed photograph with all the detail obscured. Here the argument for doing your knife is overwhelmingly in favor of naturals.
Before leaving the aesthetics, let's talk about the aesthetics of the sharpening process itself. Sharpening can be viewed as a mundane task. Rub rub rub -> sharp edge. Done. Now go cut something. Or it can be viewed as an engaging experience to delight the senses and appreciate with the senses the smell of a wet rock, the subtly of developing a fine mud with skill, looking at the beauty of the stone and so on. A sensual passionate meeting of steel and stone like paint meeting canvas. Here, naturals vs synthetics aren't even a fair contest. And my description just begins to describe this understanding of the sharpener / honer /polisher with the stone and the knife / razor / sword being worked on. All three change the other.
Although this could be considered performance, I believe that meeting the levels of perfection with a natural stone finish is more challenging in that it reveals the imperfections of your technique and the blade more fully [than with synthetics] so you work harder to perfect your final result. Scratch patterns are less hidden. Surface irregularities are brought out, etc etc. Using naturals forces you to evaluate your work more critically, hence a higher level of performance is brought out of the sharpener.
Performance. This is a more subtle argument. I have seen the argument that natural stone polishing increases the Rockwell (HRC) hardness. I don't buy this.
Let's talk about edge retention and the style of cutting edge produced. In my next post. I need a break ...