I owned the Soliloquy 6.2, and have heard the Tyler top-o-the-line Woodmere. The Woodmere is an outstanding speaker, but obviously well above the price range in which you are looking. The Tylers actually reminded me of another speaker that I've owned, which is the Silverline Sonata II. I would guess it had to do with the SEAS drivers, which are used in both. For about $2600 on the used market, I think you would find in the Sonata II exactly what you want. Considerably better hi frequency extension than the 6.2, and tight, defined bass down to 25Hz.
I find the primary difference between the Soliloquy and the Silverline (and Tyler) sound to be that the Soliloquy has a more sculpted, sharper-edged sound. Not sharp as in fatiguing, but just more carved out at the frequency edge. The Silverline (and the Tyler) sound more blended to my ear, with softer edges, and a sound that seems to just float off into the room, as the speakers completely disappear.
Where the Soliloquy hits you with a bare fist, the others put the gloves on. The impact is definitely still there, it's just that it's softened a bit, and yet with a noticeably refinement to the sound. Also, the midrange on both the Silverlines and the Tylers is phenomenal. Both are highly efficient, and can work with any amplifier. I think that for the type of music you enjoy, either would work famously. I only mention the Sonata II because they are a $6500 speaker that can be had for much less on the used market, and the performance value is outstanding.
All the best,
Howard