Integrated Tube Amp approx. $2,500

Cary Audio Design SLI-80

Rogue Audio Pharaoh II (hybrid) can be found  used for $2.5K

I’m currently using a Black Ice Audio F35 to drive my Dali Helicon 800 towers.  The 800s are only 87db efficient and the KT88 output tubes provide 85 watt output. The F35 replaced separate amp/preamp at 3 times the cost and compares well.  
 

For as efficient as your Cornwalls are I would think the F22 would be more than adequate.   
 

If you could find a used F35 that would be your best value, or even a used F22.  But the F22 is available today.   
 

I’ve been very impressed with Black Ice Audio.  

Few people recommending the Willsenton R8, I think its a good amp but not for Klipsch speakers. The Cornwall’s are too efficient for the R8 IMO. You’ll have very little volume range and the remote is too sensitive and is basically useless for the hi efficiency speaker group, just moves too fast to be useful.

Friend drives his Cornwalls with an el-kit 300b amp thast really stunning. For the money its fantastic and well within your burdget including a building service as they come as kits.

another recommended the Decware amps if you can get one they are also great amps.

Finale audio /triode labs used would be fantastic and end game amps. similarly the frankenstine 300b amp.

I second the Willsenton R8. You can buy, sometimes, direct on line, I bought mine as an open box for under 1k delivered. Many option with tube rolling (of course), and operation mode, and simple bias adjust. This was my first "quality" tube amp, There's no reason you can't grow along with this amp. I believe The British Audiophile has an R8 in his stable.