Parasound P5 + A23 vs Musical Fidelity M5si

Go with the Musical Fidelity M5Si.
My advise is since you already have a streamer/DAC you should be looking for an analog integrated amp. I recommend the Rega Elicit-R analog integrated amp currently retails for $3k new. There are other options out there. 
Naim makes really good quality streamer & DAC.

I would go with the separates.  So many possibilities for later upgrading.

I would agree with the idea of separates due to many possibilities for upgrades down the road but the separate gears that the OP is considering are mediocre at best especially for his B&W 804 D.
I’m pretty sure the Musical Fidelity M5Si will outperform the Parasound Halo P5/A 23 combo. Musical Fidelity makes very good & refined sounding gears.

However, since the OP already has Naim streamer + Naim DAC, which are very good digital front end source components, I would recommend getting an analog integrated amp instead. He won't need a built-in DAC in an integrated amp or a preamp since he has the Naim streamer + Naim DAC, which will outperform any onboard DAC in any preamps or integrated amps anyway.

This might be a dumb question, but is an analog integrated recommended even though I don't have any vinyl (anymore) -- all my music is digital.

I'm guessing the Music Fidelity is a digital amp where the Parasound is an analog amp design. It has to do with the type of amp design not the type of sources it can accept.

No, it has nothing to do with the amplifier design circuitry (whether it’s class D digital design or class A/AB analog design). What I meant by an analog integrated amp was that I was simply referring to those integrated amps that do not have onboard DAC so they only have linestage analog inputs, no DAC thus no digital inputs.
That’s what I meant by an analog integrated amp. Cause many integrated amps these days come with onboard DAC thus have digital inputs.

Since the OP already has awesome Naim server/streamer and a Naim DAC so there’s no need to get an integrated amp that has an onboard DAC.
You can run analog out of your Naim DAC to analog linestage input on the integrated amp. Just get an analog integrated amp (no onboard DAC). Cause DAC or digital-analog-conversion or digital circuitry is noisy and will potentially inject noise & interference into critical analog audio circuitry.
So pure analog integrated amp (no DAC) would be a better choice if you already have an external DAC or digital front end source components. 

Is the Naim DAC which was new in 2010 still "awesome"?  From my various conversations I've gotten a sense that there's been substantial progress in DAC technology since then(?).  

I can guarantee you that your Naim streamer + DAC combo will still outperform any current DACs in any integrated amps or preamps. Your Naim won't be able to decode or support MQA