Was thinking the Musical Fidelity M5si ($2199 at Audio Advisor) might be worth a look as it’s got good power/current with a lot of grunt and tonal density the KEFs would probably welcome. Downside is the USB input only goes to 24/96 but that’s still pretty good resolution, and it doesn’t have Bluetooth onboard but it’s easy enough to add it for little $ (requiring Bluetooth built in greatly limits your choices). Here’s a review that goes into more detail on the sound, and I think this amp may be a good sonic fit for what you’re looking for and a good fit for your KEFs.
https://www.13thnote.net/2020/10/30/musical-fidelity-m5si-integrated-strongman/