I should add combo of Statement, First Watt and Klpsch Heritage won't provide max of sound traits you're seeking. I understand you heard more of these traits with Supratek vs Statement in concert with your other existing components. Per previous post MkII and other upgrades will get you closer, as to vs Supratek, I can't say.
I don't know if should assume you were satisfied with Supratek/FW/Klipsch, but if you were, I'd first go for Linalai solid plate and see how far that gets you. Only then should you consider other pre's or upgrade of Statement.
The greatest deficiency I see in your present setup in providing for max of traits you're seeking is the FW. Klipsch Heritage and tube amps are much more sympathetic setup than SS. In defense of FW, it would be my first choice for SS and Klipsch Heritage. A 300B amp in combo with either of your present two pre's will provide all you're looking for.
I can only say my setup with Khorns, 300b or 845 SET's and Statement doesn't lack a single bit in traits you're seeking.