Integrated Amplifier for B&W 803 D3

More important than the sub itself is the integration of the sub. 
A highpass crossover is key imo. McIntosh integrated pieces should all have a built in sub highpass but read up on it. This sends the everything above the crossover to the mains and everything below to the subs. It is very hard to just pass the subs under the mains with a low pass. The results are never as good though I am sure someone who has never used a highpass with chime in that a low pass is fine….
There are external options (JL Audio C-1, $3000) but they are expensive. 
I have only tried JL Audio subs with B&W and they sounded great (seamless blend) but the electronics inside them broke multiple times. I still have the subs that were repaired. 
Don’t get me wrong SVS is fine and the upper ends subs are good just that in $1000 subs there are a number of compromises. 

I would look at the AVM A 6.2ME as the integrated amp.  Read Herb Reichert's review from earlier this year in Stereophile.  This amp is very modestly priced ($8500) intentionally by manufacturer, distributor and retailer to serve as an entry point into AVMs more premium gear.  This is an incredible integrated.  

https://www.stereophile.com/content/avm-ovation-62-me-integrated-amplifier

At that price point, $1000 for subs is a bit tight.  Take the savings from the integrated and roll it into two JL E series subs and you will be happy.  

Imo...Mcintish is the last amp id pair with B&W....Too tubby to slow,Gryphon for sure or maybe a used Boulder 

The current line of McIntosh is more neutral and the older models. Not that they are better than other things. Just a decent option. I think Mac helps take the edge off the upper mids and highs of the B&W. Just a hair soft where the B&W are hard sounding imo all in all a good balance. 
Subs crossed over to say 60hz will take some of the stress off your amps. I think people feel like they need a lot of power with 803ds because they lack bass and try to “fix” it with amps. Running subs will be a huge improvement.

Good video McIntosh vs D’Agostino, the outcome might surprise you.  

https://youtu.be/td54mT0bGo4

Having worked briefly for Magnolia and having heard top Mac gear with 802D3s and KEF Blades pretty extensively, I have to say I largely agree with what I heard on the above video. For me, poorer recordings were well served by the “beautification” of the Mac electronics, but the flip side is that it also masked a lot of the detail that makes good recordings good — depends on your tastes/goals. I will say though that I don’t find the D3 versions (unlike some earlier versions) of the 8 series to be harsh either in the treble or the upper mids but rather just very transparent to what they’re being fed — and BTW I’m not a big B&W fan just to be clear.

Which goes back back to the reason I recommended the Vitus Class-A integrated above as it gives some of that tube warmth, fluidity, and “magic” of tubes with the power to properly drive the 803s but also doesn’t hide detail the 803s are capable of conveying on better recordings. I think a good hybrid integrated would also be an excellent idea given the OP’s stated preferences.

Lastly, as for subs, yes you can spend more than the SB2000 Pros, but those subs are still very, very good and if it’s me I’d put more $$$ toward a better integrated amp as I think there’s more overall sonic benefit to be had there than getting better subs. But that’s me, FWIW.