which hybrid integrated amp sounds the most like a full tube amp?

5 years with a McIntosh MA352 and I haven’t regretted the purchase. I originally tried the MA252, but wanted the extra power of the 352 and like the blue meters and EQ. Plus more configuration options like PF settings for MM phono input.

It’s a heavy rig so make sure you have a good stand for it.

There is nothing that explicitly says you can't use a full tube integrated with those speakers but you are right to be cautious.  one of my worst demos (as a consumer years ago) was with a popular tube integrated and the 805 d3s.  

The VAC 170i which is 85w into 4 ohm taps would be an interesting choice in the full tube range.  The min impedance on the 805 D4s is 4.6ohms.  This is not brutal for any amp with 4 ohm or 6 ohm taps.  

The Octave V 80 SE with a black box or super black box and KT88 tubes would be pretty awesome here and do a lovely job.  You can add KT120 or KT150s for more power but I think it sounds better with KT88s.  This is an OTL and does not behave like a normal tube amp.  

The Riviera Levante is one of the best integrated amps I have ever heard if you can live with its 30w into class A.  The AB setting is not as amazing sounding as the pure Class A.

The Unison Unico 150 would be a good choice.  it is their flagship integrated and is quite musical.  It certainly will have the grip to handle the B&Ws.  

McIntosh and B&W get paired regularly for a reason.  They are really good together and I would never discourage anyone from that combo.  

Pathos would also be worth looking at.  They make some really good sounding amps.  I don't know exact models from them. 

Full disclosure, I am a VAC, Riviera and Unison dealer.  I have no association with the other brands. 

I have 805D4 in one of my systems and have run them with both a prima luna integrated- no problem at all, and an Audio Research REF75SE- great combo- and- the ARC btw doesn't really sound "tubey", it sounds clear with a big soundstage and plenty of bass. I also run them with an Odyssey power amp @ 150 rms. If you're looking for more warmth it may by more due to the speakers than the amp. The previous 805D3 I had were pretty dry and not very musical. The D4 cured that issue and now they're pretty neutral imo but other brands can give you more warmth. A Pass integrated or pwoer amp would be a great match for the 805D4, I had a 250.8 for a couple of years and it does have a "tubey" but punchy sound. 

I would keep things separate, and try a tube preamp. My path led me to Vintage, full featured, including two MM Phono inputs.

I start with a Chase RLC-1 remote line controller for remote volume, balance, and mute so I can retain everything wonderful from before remote control days..

A couple of thoughts for the OP:

You might consider the Vinnie Rossi Brama integrated. On the pricey side, though you didn’t specifically indicate a budget. I believe it meets all your criteria.

Had I not already been well down the road with T+A HV gear, it would have been on my must audition at home list. I’ve heard it at shows (terrible place to audition gear) and came away impressed enough that it would be a contender. Spectacular build quality and powerful enough to drive pretty much anything. 

On the warmish side of neutral and with the smoothness of tubes would be the T+A PA 3100 HV. While I’ve gone their separates route (a decision driven by purchasing their DAC w/ a preamp built in), I had one in system for a couple of years which i thoroughly enjoyed. Like the VR, spectacular build quality and enough power (and current) to easily drive anything. The T+A HV line has a warmer sonic quality than the Hegel. I’m familiar with the Hegel sound as I own one in a TV theater system. Great gear.