Integrated Tube Amp approx. $2,500

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. 

+1 on the Octave 40SE. 

If you only need an integrated for component switching and not a DAC or phono stage, I would go with a small builder like James Burgess.  Ask him to install a selector switch, shouldn't be  hard.  I just had a Burgess and it was a very very nice sounding amp.  Lot's of small builders, including Had, could probably get it done in your budget.