Its quite refreshing to see so many positive comments regarding all of the speakers concerned. Often when one asks a question (such as your own) it will meet with highly partisan, non-objective comments and recommendations - Kudos to all of the thoughtful respondents.
My own immediate thoughts (after reading the thread): Have you been able to bring any of these speakers home for audition? If not would you be able to? You're spending quite a bit of $. I would think that any dealer relieving you of this much $ would be happy to oblige you.
So much of what you hear is system/room-dependant that it'd be a shame if you didn't actually get a few of these fine speakers home for a good weekend-to-weekend listen.
The character you are hearing at the dealer will most defiantly be different than it will in your own system. Even simple things often overlooked such as speaker cables and ICs can take a speaker from sounding brutally analytical to heavenly musical.
Additionally:
Speakers such as the W/P-6s are extremely fussy about positioning and can sound dramatically different in two different rooms. A Wilson dealer should be willing to show you how theyd sound in your space.
Ive never heard the Amatis, I have heard the W/P 6's, the Eidolons - and the Circes (that Larryro mentions).
Delivery of sound from each is quite different. The least-mentioned Circes are wonderful speakers and really should be considered in your audition (probably the Kharmas too). The Circes are especially wonderful with tube gear. They are very open, with three dimensional soundstage that lives and breaths Id call them the closest to an electrostatic or magneplanar but with dynamics
and no need for head-in-vice listening! One can walk around the room and still point to a given instrument or musician in a swing/jazz band. The Circes lack the dynamics of the W/P, but this is true of so many speakers including (but not limited to) all other speakers on your list. That said, the Circes will get down pretty deep, and with some fairly articulate bass lower than the Eidolons & just as tuneful.
The W/P are impressive in their speed, dynamics and HUGE soundstage. I've never heard them on CJ gear - most often they are paired to beast SS amps from Krell etc. But what I have heard from those systems is nothing short of remarkable. If it were me I would HAVE to bring them home just to be sure.
The Eidolon's - which are much talked about, and come very highly regarded, do just about everything right, but need lots of juice! In contrast to the Circes the Eidolons image equally well, with a very natural presentation - but not quite as natural as the Circes. The Circes just seem more organic in sound quality start and decay. In the bass, the Eidolons have neutral & tuneful bass, but not as quick, deep or snappy as the W/P's. Where the Eidolon really shines is in the midrange/highs & ability to disappear. The Eidolons ability to plausibly recreate the human voice may be without equal.
What a truly difficult decision... and one that Id love to be in the position to have to make ;)
Thanks for the thread, & be certain to post what you end up with.
Cheers,
Mike