You can do what you wish. Its your money. But I highly recommend taking a different path to achieve your goal. The speakers you are looking at are very revealing, and not all that forgiving. When you say that the speakers will sing with more power, that can be true, but its only 1 small piece of a much bigger puzzle. For example, you can find 10 different amps that have enough power to easily drive your speakers, but all 10 will sound very different. At this level, component matching is everything.Do you care to list the associate components in your system driving the Andra IIs? I'm curious what made it unforgiving.
One thing I can tell you for sure, is that if you are going by reviews, professional or otherwise, the components you read about won't sound the same when you actually get to listen to them. Sometimes they sound close to what the reviewers say, but sometimes they sound completely different. Its a very risky way to shop.From my experience, I found Paul Bolin's Stereophile review dead-on. http://www.stereophile.com/floorloudspeakers/719/
I had Andra II for 5+ years. It's NOT analytical or too revealing but very musical with the amazing Morel midrange drivers and Esotar tweeter. Only problem I encountered is a midbass hump but was able to tame 99% with proper associated components.
I found high powered SS amps worked best. I had a 275 wpc tube mono but still no match for SS. In your budget, checkout Pass X350.5 (Reno HiFi had a refurbished in $5K range), Krell 302e, Parasound JC-1 mono and McIntosh MC501. Krell FPB600 was awesome but SQ was unrefined compare to latest.
I had many SF preamps and found the more neutral Siemen and Telefunken e88cc worked best with the Andra IIs.
As far as cables, I found ASI Liveline ICs and SCs worked best. Settled on 2 pairs of ASI Liveline SCs. SR Apex was also very good but no match for ASI and much much LESS $. I heard many found Nordost Valhalla also a good match.
Ideally it's best to demo before purchase. Speakers are tough to ship and I bought mine new but buying used, it's a very low risk IMHO. The only reason I replaced Andra was to try something different.
I'm not familiar with Wilson Sophia II so will refrain from commenting.