Need recommendations for better two-channel audio out of my Marantz SR-6005 and my B&W 683

The SR-6005 is a really older generation Marantz receiver.  It uses the previous generation HDAM audio stages, which have slow slew rates and, as a result, have a very warm and slow sound.  The newer generation Marantz receivers are better.

The Anthem make excellent HT receivers, but the sound is going to be the complete opposite of what you hear now.  The Anthem are extremely high resolution and will sound very exciting and dynamic with movies.  Music is likely to sound significantly clearer, but on some systems the Anthem can come across just a bit bright.  It really depends.  You can give it a shot from Crutchfield and see how it sounds in your environment.

An amplifier could improve things, but you are still limited on the preamp section of the Marantz receiver.

A new Roku or network streamer is likely going to make very little difference in your equipment setup, so I wouldn't spend any money on that right now.

Thanks for the input. I'm leaning towards the Anthem. There is a dealer nearby so I could support my local shop. They also sell B&W, so I might get to demo it. 

Get an integrated stereo amp and plug the L/R pre outs from the 6005 into it and you’ll cut the AVR completely out of the system for 2-channel.  There’s a Yamaha AS1200 at Accessories4less for $1899 that will significantly outperform the Marantz across the board.  Best of luck. 

#1 First things first,
Get rid of the lousy Klipsch sub and get two Rythmik sealed servo-controlled L12 subs The price is 1060 usd shipped (530 each). This alone is a great future proofed upgrade for music. No matter where your upgrade journey takes you, these subs will continue to stay. Keep in mind, the subwoofer is essentially a speaker and it has significant impact for music next to your 2 main speakers, IF you have the right ones.
http://www.rythmikaudio.com/L12.html

#2)
If you insist on keeping the receiver in your 2 channel system, get a Marantz PM8006 integrated amplifier. It has a power amp direct in (bypasses the preamp) that you can connect to the receiver pre-outs. See how it sounds. You could also get the pm8006’s preamp in the chain, run your calibration and see how it sounds. The advantage here is you get to keep the bass management from your receiver.
Here’s a factory refurb with a 3 yr warranty for 850
https://www.accessories4less.com/make-a-store/item/marpm8006/marantz-pm8006-2-ch-x-70-watts-integrated-amplifier/1.html

#3)
If you’re still unsatisfied, lose the receiver altogether for music listening, get a Marantz NA6006 streamer and connect it to your PM8006. This is a great sounding streamer+network player+DAC+Preamp at this price.
Here you go, factory refurb with warranty for 500 bucks
https://www.accessories4less.com/make-a-store/item/marpm6006/marantz-pm6006-2-ch-x-60-watts-integrated-amp-w/d-to-a/1.html

The NA6006+PM8006+your speakers+ 2 Rythmik L12s will get you golden once you take the time to integrate your subs properly (it is difficult without bass management, but, you will get there)