Musician vs. audiophile

You did not state what power amp? Assuming it is a BAT too but who knows.
Now I must state from personal experience and a number of other comments I have read that BAT and Wilson speakers are usually a marriage made in heaven IF everything else is correct. I have no experience of the BAT preamp but I use a BAT power amp to drive my Wilson's and I am wanting for nothing. Imaging and soundstage are superlative and bass response can cause bowel movements....lol.
Even at low levels for evening duty I am losing nothing and flat is not a word I could ever use.
Als suggestion to disconnect the subs is excellent and the first place to start. 
You also have no mention of source? Streaming, CD,vinyl?? Could be numerous issues there too.

What kind of wires are you using ,vs the ones at the store ?
that too can have a big effect.how about your source?
is it the same ? These 2  things can  make a huge difference.

Open discussion forums can be so interesting at times as people describe their listening experiences.  Czarivey and uberwaltz couldn't be more different in their assessment of the Wilson speakers. Subjectivity allows such a very broad spectrum of impressions.
Charles 

The Sophias are anything but flat, punchless and colorless.  Even with an average 250w ss amp ( assuming no impedence mismatch) and a BAT tube front end, the Sophias should give you dynamics and color. 
Either amp/ preamp mismatch, poor setup ( Wilson’s should be toed in so you can barely see the inside of each tweeter portion of the cabinet at your listening position) or cables. My $ is on bad positioning which will make the Sophia’s punchless, colorless and sterile.I agree that a Wilson dealer rep should be hired to have a look. They are truly great speakers if set up right.

Exactly Charles.
Indeed one of the members here might listen to the ops rig and not hear "flat" at all!
However deep down the only opinion of how it sounds that counts is the ops( and his good lady of course) so if flat and uninvolved to them then a fix is to be found.