Integrated Tube Amp approx. $2,500

Skunkie Designs Electronics did an extensive series of tear downs and reviews on both the Willsenton R8 and the Muzishare X7 over a period of months. It seems Willsenton took some of her feedback to heart and changed a few things in their circuitry to make it better as she suggested.

Here is a link to one of her videos. But note that there were other ones later where she applauded Willsenton for upgrading their design for safety.

Even so, while she liked both of these at the end of the day (after mods) she stated that well, nothing in life is free, and the quality of the transformers on tube amps means about as much as the quality of the tubes. Neither one of these is a "giant killer", but they are nice at their price points. Many people have bought them and enjoy them. 

https://youtu.be/fjGefU2qB-0

Oops - integrated, sorry, Elekit is a power amp... nevermind.

You own a pair of Klipsch speakers which tells me that you like rock. Rogue Audio Cronus Magnum would probably rock out with Ks. It’s an honest well-priced product to boot. 

Look into a Dennis Had Inspire.  Dennis founded Cary Audio, retired and now hand builds small SET/SEP amps and pre-amps out of a small shop in Cary, NC. He sells them through ebay under radioman731.  They pop up every now and then, currently he has a NOS 807 SEP amp for $2,800 and a 6V6 preamp for sale.
 

He built my KT-88 with a volume pot so no preamp required.  If your DAC has a preamp volume function you can use that too. The KT-88 drive my Forte III terrific. Superb soundstage and tonality.  Plenty of juice to drive Cornwalls to reasonable SPL which have higher sensitivity than the Fortes. I park it in my bedroom rig now where it drives 90 dB Vienna Acoustics Bachs just fine. Sweet little speaker btw.
 

I concur the R8 @40 wpc too much for Cornwalls, plus it’s a PP, SET sounds much more real with Klipsch Heritage IMO. I park a Willsenton R800i 845 in front of the Klipsch now. At 20 wpc I have inserted an XLR 10 dB attenuator at the balanced input in order to have more volume pot range, but have never gone past 12 o’clock @80 dB peaks. 
 

Look up Lejonklou Boazu. It’s an amazing sounding integrated and the used price is exactly in your price range. It’s dead quiet so perfect for high efficiency speakers like your Cornwall, detailed and not fatiguing at the same time. It’s very minimalistic in design and features but it still has remote control.