Musician vs. audiophile

Solid equipment, sounds like its time to start with ancillary areas like speaker placement, room treatments, racks, and cables.

Before changing out components!

The Wilsons and the BAT are somewhat dull sounding to my ears. Both together can't have the greatest presence. I remember the same with Classe and Aragon amps. 
A few experiments you could try:
The subs may also be coloring the sound. Remove them.
Toe in speakers so tweeter is pointing at your ears. 
Replace your interconnect cable with a Belkin Gold AV cheapo from eBay in case your cables are a problem - most are. Replace your tubes with EH or Gold Lion.

First...I agree mostly with Charles to trust your ears :) , but when you have a significant other involved, you may need to compromise.

I suspect your wife is like my wife (also a musician), she prefers speakers that are more natural sounding like Harbeths, Proac, Magnepans, Quads or Vandersteens. Wilsons and Magico are very much audiophile speakers, if you ask me. It’s really a matter of taste, preference and compromise. For me, I appreciate both types of speakers.

My wife really really liked the sound of the Harbeth 40.2 but I didn’t have the funds at the time and she wasn’t big on putting speakers on stands. I was using a pair of Harbeth C7ES3 at the time.

At the end, it was a comprise on multiple fronts, price, aesthetics, size and most importantly sound. We ended up buying a pair of Vandersteen Treo CTs. Per my wife, the speakers made the piano sound right and very natural (the price was right too). :)

Have you listen to higher end Vandersteen speakers? A nice comprise, if you decide on looking for speakers again could be a pair of Vandersteen Quatro CTs or the 5A Carbons. Both speakers have active bass and both sound wonderfully natural. The Treo CTs are passive and bit light on the bass, but they hold their own, plus you have a pair of JL subs to add into the mix. Check them out, if you have dealer close by.

I suspect that an impedance compatibility issue is contributing to the problem. Your BAT VK-3iX (I assume that is what you meant) has output impedances for its XLR and RCA outputs that are very high and that also vary widely across the frequency range, at least if your unit does not have the optional Six-Pak upgrade. From Stereophile’s measurements:

The VK-3iX’s output impedance was also high, and this might well have an effect on sound quality, depending on the input impedance of the partnering preamplifier [I assume he meant "amplifier"]. The unbalanced source impedance varied from 7k ohms at 20Hz to 1460 ohms at 1kHz and 2650 ohms at 20kHz, while the balanced figures ranged from a very high 14k ohms at 20Hz to 1850 ohms in the midband and above.

You didn’t say what amplifier you are using, but those numbers definitely indicate that sonic issues **will** arise with many and perhaps even the majority of solid state amps.

Also, I suspect that like most JL subs your subs probably provide only line-level inputs, and you are either driving the power amp from the preamp’s XLR outputs and the sub from the preamp’s RCA outputs, or vice versa. Many and perhaps most preamps providing XLR and RCA outputs do not drive the two pairs of outputs from separate output stages, and the signal provided to the RCA connector for each channel is the same signal that is provided to one of the two signal pins on the corresponding XLR connector. If that is the case with the VK-3iX the input impedance of the subs and the capacitance of the cables to the subs (especially if those cables are relatively long) can both have audibly significant effects on the signals received by the main power amp, that are reproduced by the main speakers. So if you already haven’t done so assessing the sonics provided by the Sophia with the sub cables disconnected from the preamp may provide useful insight into the issue.

Good luck. Regards,
-- Al

The McIntosh amplifiers, particularly the ones with Autoformers, pair very well with Martin Logan ESLs, according to owner feedbacks and my own experience. They are hardly considered "box store" quality. No experience with your other components.