Hello OP, you have options here. BUT maybe read the END of my post first..:-)
Plug the Class D into a passive preamp or the Schiit (I haven't use the
Schiit). That is a high crossover point. DON'T plug your Valve amp into anything BUT the HF on board crossover of the speaker. Nothing else.
They may seem to sound better/worse, be patient, let EVERYTHING settle.
2.5K and down WILL benefit from a separate tone control, The Schiit if it has an EQ that would really be nice add a little bump in the mids and volume control.
That is what I do. I use a Behringer product (2496). I control everything from 300hz down with full blown DSP/Servo. 300hz UP, onboard OX of the speaker is perfect.
END:
Don't be surprised though, something about valves and you said it yourself.
"my 2.2 system today sounds superb for me (I've heard some much more expensive ones sounding much worse)".
250 hz to 2.5K that is THE sweet spot for me, child of the 60-70s
If you can live without "sugar sweet" valve doing mids..
I can for the summer months. I also can't wait for fall, right NOW...to change back to valves, though...
Just sayin'
Regards