Pursuing clean sounding tube gear is a fool's errand in my humble opinion.
Aim for even harmonics dominated THD of around 1~5% for obvious tube saturation 'magic'. This most certainly means very high plate voltages. There, you will feel the tubes 'boiling', 'alive', and reacting properly to input signals. The vocal range becomes seriously boosted and pleasantly warm (like radio hosts), the highs past 5Khz get that typical sizzly distortion, you start feeling reverb tails getting boosted as if you had a compressor/expander active. It's that selective, amplitude-dependent boosting and cutting that creates the typical 'holographic' tube sound in my experience.
The currently available tube preamps and headphone amps are way too clean for any meaningful tube sound. You'll only be getting linear tube frequency response alterations at best. Indeed, even sound demos of beefy looking all-tube OTLs like TA-26S, Darkvoice and the likes prove my point. Yes they sound different (worse) than solid state, but nothing like a properly driven tube circuit.
I am sharing here the distortion graph of an extreme example of a DIY 12AU7 design with high plate voltage of mine, with gain turned all the way to the maximum.
This is quite excessive, but it is to demonstrate the possible harmonics range all with very low noise floor. By turning the gain knob down and compensating with the volume knob, you can get a very musical experience with H2-dominated distortion in the neighborhood of -60 to -40 dB, a sound that's quite honestly impossible to get even with the latest and greatest Fabfilter and NAM tube emulation/saturation VSTs on the computer. I've tried for months... Yes you can get the harmonics on point, but other aspects fall short.
Sorry for the long, practically blasphemous post praising distortion. But hey, one can appreciate both a super honest, clean SS as well as a sizzling tube tearing through their signal chain, which, tl;dr, is pretty much non-existent with modern tube designs.