Please help: Do I need a preamp?

The SOUND you are hearing is what is usual for a need for a real preamp. I would recommend getting the preamp, or at least borrowing a good preamp to see if that can fix your problem.

Norbert, I don't think it's an impedance mismatch because I believe the BAT's input impedance is on the high side and I'm sure the ML's output impedance is low enough not to be a problem.

I don't believe that using a tube CD player or preamp will solve your problem.

Two things I would try are experimenting with speaker positioning and experimenting with different system cabling. The Virgo IIs are VERY sensitive to both of these variables. Another viable option may be to incorporate a quality subwoofer if the above measures fail to satisfy...

It's too bad the Virgos are not biampable, because they seem to like the power and control of solid-state in the bass. I used to use tube/MOSFET hybrid amps with my Virgos and just going through the single input tube softened the bass although it sounded fabulous through the midrange and high frequencies.

I'm now using an Aragon 8002 amp, which has great control in the bass and with the right cabling, sounds quite detailed and musical throughout the audio spectrum. The detailing in the highs is particularly impressive. In my case, switching amps resulted in both performance and financial benefits.

I DON'T KNOW YOUR SPEAKERS BUT ALL LOOKS OK.
MY 2 CENTS
I WOULD WORK ON CABLES FIRST, MY EXPERIENCE WITH THE STEALTH WASN'T GREAT, IC'S -SO TRY SOME KUBALA EMOTION LINE/ VALHALLA/PURE NOTE VERSION 4. SPEAKER CABLES TRY KUBALA EMOTION / JENA VALKYRE/ TRANSPARENT REFERRENCE. SEE WHAT THAT DOES. YOUR ML 39 IS OK THE BAT IS OK, SPEAKERS ?

You could try a good pre-amp. A good pre-amp is always a good asset in any system.

I think that cables could be an issue here.

If possible try either IC's Kubala-Emotion/ Valhalla/ Pure Note version 4.

Also I would try the Kubala Emotion / Jena Valkyre/ or the Tranparent Reference speaker cables.

my 2 cents