Advice on Integrated Receiver

Get that Schiit out of your audio chain and replace it with a decent phono stage. 
I’d start there. That’ll be a bottleneck no matter what your amplifier or speakers are. 

Ok solve two problems at once - your integrated and your Schiity phono stage:

https://www.usaudiomart.com/details/649883010-luxman-l-509x-integrated-amplifier/

Fair price for this should be around $5k - $5500 all in, tops. Given the few small nicks that live on the side of this integrated. Also comes with a phono stage that will send the Schiit to the garbage 🗑️ 

And btw I do not hate the schiit mani. I had it. Know exactly what it is and what it’s worth.

B&W 800 series will be very nice - D2 or D3.  
They sound engaging and will draw you in. 804 or 803 for that size room most likely is all you need. However, they like power and require careful matching when it comes to the upstream components. Can’t have anything upstream that’s on the brighter side and or that emphasizes the presence region. When I had the N803s I had them paired with Pass Labs X250.5 and Audio Research tube preamp.
I think you’re pretty much looking at an overhaul.

If you want to go the integrated route, Pass Int-250 (would be my first choice) or Hegel H390, Hegel H590 or the Luxman 509 (slightly underpowered for the B&Ws IMO).

As for the phono stage, I like Sutherland for sound and flexibility. Even the bottom of the line KC Vibe MkIi is excellent.

Just my $0.05 of course, you will get other suggestions so start compiling the info.

Yeah the 💩 is holding you back. A better phono amp is a good starting point. Then continue assessing and continue on from there.

Preamp is a critical part of the system. It must be transparent and on the level of your amp. Unless it’s a makeshift solution until you get a good preamp, I wouldn’t use the Cambridge in that capacity if you want to go the separates route.
 

But, with a budget of $5000 you’re better off with an integrated in my opinion. So I would sell Cambridge and the 💩 and get a good integrated with or without a built in phono stage.  Any of the integrated amps mentioned above, Parasound, Luxman, Hegel and Pass will take your system to a new level. The speakers you have should let you start enjoying the music.

H390 should be good. Gives you streaming capabilities as well. Add a good phono stage and you’ll be all set. 

@bound4h looking at it from another angle, you get a very nice phono stage with the Luxman amp that will be good enough until you are ready to upgrade. Something that isn’t included with the H390. If you can swing it, get the luxman although like I said earlier, the Luxman might just borderline for the B&Ws as far as power is concerned. It should sound great though, regardless.