You seem to be in the market for an ultimate knife. Would you be as interested in "all the performance but less money?" Or are you really pointed towards the pinnacle?
By way of example, I'd be really torn between a Konosuke HD (at the very low end of your proposed budget), and a Masamoto KS.
Since you're seriously interested in carbon what about the Konosuke White #2?. White #1 is all well and good, but as far as I'm concerned a Konosuke gets sharp enough even without the tiny extra boost a really competent sharpener can extract from a Fujiyama; on the other hand, White #2's edge holding and added toughness is something everyone can appreciate, AND they run about $150 less. FWIW, if you love the handle, you can certainly get custom handles both from Konosuke and from OEM handle makers.
You might also consider the Tadatsuna wa-Western knives, whether "G3" or Shiro #2.
Then there are the Richmond and Moritaka KS clones in various flavors of blade alloy. Certainly, they're at least worth considering.
Be aware, a Takeda is a Takeda is a Takeda. For that matter, the KS clone aside, a Moritaka is a Takeda is a Takeda, too. With their very flat profiles and ultra-thin, cladded, AS construction they have a particular feel and action, that's different from the other knives on your list.
And that begs another question:
- Rather than giving a list of rarified knives, can you articulate the attributes of what you really want?
Plus, when you talk about knives of such a high caliber you can't get away from the reality that they all need very competent sharpening or they lose their dearly priced advantages.
So, another couple of questions:
- Are you already a good sharpener? And,
- How are you planning to sharpen?