How much do you have to spend?

Very happy that I paired a HIROSE RS-520 with the Cornwall IV's. The capability of the RS-520 will meet audio needs for years possibly decades to come. 250W with Klipsch speakers is a bit of an overkill but the HIROSE is extremely clean. Highly recommend it. The combo is a simple one and done setup. 

I wouldn’t spend $10k on new speakers if you’re planning on keeping the NAD.  Also, I’d buy Joseph Audio Pulsars over the KEFs, but that’s a personal preference thing.  Just my $0.02 FWIW, and best of luck. 

Room configuration and speaker placement necessities are key to system synergy. You can have great gear and still fall far short of excellent performance. Your amp is said to be a weak link, but to me trying to get a full musical picture from a pair of 5” woofers is not a realistic possibility. Within your constraints, add cone area!  MoFi SourcePoint 8s are a good option. And use Dirac Live to create a fully integrated in-room response with your subs. 

1st rig ($6k): $1.5k speaker, $1k amp (used) / preamp, $1k Dac, $1.6k streamer & $0.9k cables.

2nd rig ($5k): $2k speaker, $0.7k int. amp (used), $1k Dac, $0.6k streamer/lps &0.7k cables.

Yes you can easily put a good system for 10k. My friend spend 10k , Galion Amp tsa 75 $1500, galion tsp preamp $1805 , Focal floor standing speakers for 3.5!k, advance Paris cdp $1400.plus cables and cabinets and room acoustics.It sounds. It sounds good to my ears.He does not care about diminishing returns.