Tubes or stick with S/S

I switched in January this year from refurbished Dyneco monoblocks to a Primaluna Dialogue HP powering Tekton speakers with 95 or so db sensitivity.  The PL is really some amp, loving it.  However I want to add that although I'm not familiar with your Cornwalls from this thread it seems they are efficient and some advice was that you can go with a lower powered tube integrated.  I have my system ina fairly large room with a high vaulted ceiling and I sometimes like to listen loud.  Upscale thought I'd be fine with a regular Dialogue at 36 watts but my Dynecos were 60 and barely doingbit so went with the HP at 72 watts and I've used every watt.  I've had it turned up almost to full a few times, depending on the volume of the source recording. If you like to occasionally recreate a live rock concert at home then don't be shy about watts.

Manley Mahi Mahi monoblocks.  Beautiful sounding, quick as hell with great imaging and natural timbre.  Vocals and acoustic instruments sing.  Can be found for about 2K used.

Several customers of ours have commented to us that our M-60s make the Tannoys sound the best of any amplifier they've tried. I get these comments but its rare that they tell me what the other amps are. It does appear though that if the amplifier is low distortion that the speaker benefits from having more power. When the power is clean it does not sound loud- IMO/IME that is a sign of a really good system.

If I had a pair of the K-horns, only one place I would be looking for an amp....one of Dennis Had's Inspire Single ended KT88 amps...they work great with efficient speakers.

Go with tubed OTLs with higher power. 30W per channel as a minimum. In my experience, OTLs are in another league when you compare them against SET and push-pull designs on higher impedance speakers.