mono amp advice

I am trying to match a set of mono amps to my system.
System consists of- BAT 31se preamp, Ayre C-5xe player
and Wilson Sophia 1 speakers. Price limit is $10,000/pr.
I was thinking of Cary 500MB, Parasound Halo JC1, Boulder
850... I prefer s.s. but I am flexible. Any thoughts or
advice would be appreciated. Thank you.
With the Sophia's large bass driver, I would recommend staying with solid state to better control the bass driver and allow the mids to sound their clearest.

Although a bit higher than your budget, the new Metronome AMT-70 Class-A mono amps ($18k/pr.) are extraordinary!

jim Ricketts/tmh audio
A couple of used Rogue Zues' would be great. Although they are stereo amps you could biamp if the Wilsons are such.
Lots of great options - of the amps listed I would go with the Boulder. I'd also take a set of 7B-SSTs over the JC1s since you have short-listed them. Just my opion. I have a similar set up, and am thinking about going to ASR Exclusive II...maybe. More listening to do first.
HI there the legendary George Kay has reissued the Moscode hybred amp. It has a mono switch for vertical bi amping. You will have the best of both worlds, and none of the drawbacks.
Another bonus the amp is visually stunning. George also offers a 30 day in home trial. I owned a moscode 15 years ago it kicked ass. I am going to get rid of my Audio Research mono blocks for a pair of the new moscodes.I also understand Wilsons are difficult to drive. Good Luck Timothy
PS a pair retails for about 10,800. I am sure if you buy a pair he would discount them to work in your budget.
Thank you for your responses. I have added
Theta Enterprise,Simaudio W10 and Musical Fidelity
kW750 to my "short list".