I too use and love my Ayre K-1xe preamp, and plan on keeping it for a very long time as well. (The phono stage makes this an incredible value as a full function preamp, IMHO!) Its neutrality and transparency is incredible.
However, I too found most solid state amplifiers to be somewhat lacking in bloom, especially in the mid-range. (Perhaps having a solid state preamp with a solid state amp is just too neutral.) I found my long term amplifiers when I bought my Lamm M2.1 (200 wpc) monoblocks. These amplifiers are hybrid amps, with just one 6922 tube in each amp, but that one tube just seems to add a sense of life to the music. (FYI, replacing the stock Sovtek 6922 with something like an Amperex Orange Globe 6DJ8 ($200/pair), or better yet, the Amperex pinched waist 6922 ($400+/pair) will really make these amps sing!)
I used to use these amps with my Revel Studios, (which I felt sounded similar to the original Sophia), and now use them with my Eggleston Works Andra II. The Andra II speakers really have great bass response, and these amps provide all the power and bass extension I would ever want. (The M2.1s have better bass response than any tube monoblocks I've ever heard.) Their mid-range is fantastic, with a nice touch of tube bloom. (Vocals are great!) Their treble response is great, with good extension and lots of decay to cymbals. (Note: with the stock Sovtek tubes the sound has just a slight touch darkness. However, with even decent NOS tubes, this touch of darkness is no longer present.)
I got my Lamm M2.1s used for $7K. The Lamm M2.2s (220 wpc) replaced the M2.1s, and are slightly better in the treble response, but tend to run slightly over your $10K budget @ $12K used.
My two cents worth.
Good Luck in your search!
PS As an alternative, the DarTZeel NHB-108B, (The "B" version has balanced inputs), is a mighty fine solid state amplifier, and might do the trick if you can get by with 100 wpc. Used they run about $12K too.
