Anthem A5 enough to drive B&W 804D3 fronts and HTM1D3 Center?

I would think that the Parasound Halo A31 would be a better power amp than the Anthem A5. 

Re the hiss you heard from 2 feet away IMO there might have been something else in the signal path somewhere in your audio chain eg your preamp, kind of interconnects (single-ended or XLR), speaker cables, power cables, AC power line or AC power product, front end source component(s) that are the cause......again it's possible but I don't know for sure and can't confirm. But usually the noise floor is determined by your amp, but who knows something else might have contributed. 

What at preamp are you using? What front end source component (digital or analog eg turntable) do you have? What kind of cables are you using? it's very likely that your AC power line product or your main AC power line in your home might be the source of the hiss that you heard from 2 feet away. Is your main AC line off your wall outlet grounded and do you have a dedicated line? What kind of AC power product are you currently using? 

But again I've never personally heard the Parasound Halo A31 before but my buddy and many other people I know have and they said it is a great amp especially for the money. And the SNR of 112db on your Parasound A31 is a good number and in theory the noise floor should have been pretty low. 

The power output rating of the Anthem A5 at 180 wpc @ 8 ohms will be enough power to drive your B&W 804 D3. These are pretty efficient speakers and aren't hard to drive assuming you have good quality clean amplification and not using some AV receiver. 
But I would think that the Parasound Halo A31 would be a better amp than the Anthem A5. The Halo A31 is highly regarded and received high recommendations from various different hifi reviewers or magazines / publications. You can never go wrong with this amp. 

Another good amplifier option for your B&W 804 D3 will be the Classe Sigma Amp2 stereo power amp or the Sigma Amp5 give-channel amp or the higher end series Classe Delta CA-2300 stereo amp or the CA-5300 five-channel amp. Even the lower priced Rotel RMB-1585 five-channel power amp will have great synergy with your B&W as well. 

Thanks so much for the detailed reply.  You asked a couple of questions that I'll answer.

On the hiss, I've tried everything to get rid of it.  I've (a) used a cheater plug; (b) swapped for very expensive Audioquest MacKenzie RCA interconnects; (c) bought a Furman elite power conditioner; (d) unplugged the coax entirely; (e) unplugged all components except the amp (and it still hisses); and (f) lowered the gain on the amp (this brought the hiss from 2 ft down to 10 inches, but the negative side effects on speaker volume aren't worth it).  I spoke with Parasound about it, and they believe that it's a characteristic of the amp floor.  Others on other forums also have had these issues with the amp.

I'm using a Denon x7200wa as a preamp, though the end goal is to get a Marantz 8805 or an Anthem once HDMI 2.1 boards are installed.  My source is Tidal a (very high-end) home theater PC.  It's connected to the Denon with a digital coax cable for audio (and HDMI for video).  The digital coax is a generic cable from Amazon.  Everything is plugged into a Furman Elite 15 pfi power conditioner.

To be fair, the noise floor is pretty low in the sense that I absolutely cannot hear it from where I'm sitting in the room.  I sit between 8 and 9 feet away, and the noise is absolutely inaudible after 2 feet.  And even then, it's inaudible over 1 foot except at a height right in line with the tweeters.  So really, I may be letting the perfect get in the way of the good here.

As to the Parasound, I agree that it's highly regarded.  I picked it because the first 7 or 8 watts are pure class A, which is unheard of at its price for an amplifier with 250w RMS all channels.  I also got a good deal on it.  But that deal came with a price -- it's basically unreturnable because it was a special order.  The store is making an exception and will let me exchange it for an Anthem MCA 525 (for an additional $600), an Anthem A5 (for an additional $1100), or the Rotel RMB-1585 (even trade).  I also could go for any other Anthem, Rotel, Parasound, or Mark Levinson product, but there were no other similar choices in the price category that I'm looking at (and they aren't a Classe dealer).

With those choices, I don't want the MCA 525 because I've read a number of posts (and verified with Anthem support) that it sometimes sends pops to speakers when it turns on and off because they removed some sort of relay.  I don't want the Rotel because I previously auditioned a Rotel RB-1590 (the big 350w 2 channel one) and found it inferior to Parasound in sound quality -- I suspect that the 5 channel one isn't as good.  

That leaves the Anthem A5 or just sticking with the Parasound.  I'm on the fence.  I don't want to lose sound quality, but I'd like to get rid of the hiss for peace of mind.  It seems rather silly when you stop to think about it, though -- I hear the hiss only when I get very close to the speaker, yet I hear the sound quality and use overall amperage/wattage of the amp every day.

I really appreciate your thoughts.