Integrated Tube Amp approx. $2,500

If you’re looking for a more neutral sounding tube integrated this Octave V40SE if still available is excellent and well worth a look.  Best of luck. 

https://www.ebay.com/itm/226058312309

You know, you don't want to go too cheap on a tube amp. I would want something you can get serviced in the USA. The Prima Luna 100 is near your budget. You also want to be able to afford tube replacement when the time comes. The Prima Luna would work very well with your Cornwalls, plenty of power. For your first try at a tube amp you want one that will have no issues. Then you get try other things.

I do have to say I heard the line magnetic at my local hifi shop (Northern Audio in Pittsburgh). Not sure what model but damn does it sing!

I bought the line magnetic tubed CD player from NA and love it! Super well built.

I’m by no means an audiophile expert and have a modest system but I have no problems recommending the Black Ice integrated. When I decided to dip my toes in the tube waters, I bought a Jolida Fusion 6802 which is the predecessor to the FX22. I’m running it with EL34 power tubes. I’ve had It five years with no problems. Although I have loaded it with NOS tubes. I’m very happy with it and have no desire to move away from tubes.

Cary Audio Design SLI-80