How much do you have to spend?

I don't know much about NAD, or never heard anything exciting about them that would make me try them. KLH speakers, yes, but I agree with the comments above, it's a too many tricks pony, it would be first to replace on my list.

Naim Uniti Atom all in one everything,$3500 do $3500 for speakers you are done if you stream only..

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.