Best amp for B&W805D3?

its nothing to do with the amps. its the tweeters. you will need to remove the crossover and retune them. They have too much highs. 

A friend is running a Musical Fidelity M6si Integrated to great effect with the B&W’s. Her system sounds very nice. Don’t touch the tweeters...

I am wondering if it is the additional power that is helping? I am also wondering if I need to switch to SS?

Yes!!! Tubes don’t generally work optimally with B&Ws unless you pay up big $$$ for lots of tube power. IMO you’re much better off going with a tube pre and a Class A (or similar sounding type) amp. Something like the Unison Research Unico Due integrated would probably give you most everything you’re looking for, just to throw one possibility out there. Hope this helps, and best of luck finding something that works well for you.

Some time ago I tried a number of amps on a pair of 805-II (i.e. a previous model).Driven well you should have clarity rather than harshness.
I can confirm what is said above: a class A SS (or a good AB) will drive them well -- a MF nuvista integrated, a Pass 60, and ATC integrated, etc. All  reasonably priced and great performers

If you insist on tubes, the only amp I tried with (remarkable) success was a CAT -- which is ruinously expensive, but gave the best sound!

It is not possible for a speaker to have "too much highs". What is possible is to reduce all frequencies BELOW the uppers which gives the illusion of exaggerated highs.
My 804D3s are having a continuous love affair with a BAT VK-255SE amp. Give this insanely reasonable (used) amp a try (with a good tube pre). 

There are tube integrated amps that will work wonderfully but...like others have said, the price tends to be a bit higher.

It is definitely a mater of taste, but if the PrimaLuna is drifting bright, my hunch is Musical Fidelity (other than NuVistas) would be a dreadful choice.  That being said, the NuVista Amps would be a lovely choice and a good match.  Tube input stage and SS output stage.  The Nu-Vista 600 is more power than you need and is $6990.  

VTLs IT-85 integrated would be a first rate choice.  Those are hard speakers to drive in terms of impedance but don't require a ton of power so 60w should be good.  This is stable at 2 ohms.  Good luck finding a current price for it on the web.  One ad on US Audiomart sayd $5500 but who knows.  Not sure why letting consumers know what your product costs is so upsetting to manufacturers.  You will need to call a dealer.  

AVM is warmer in sound profile and the Evolution A5.2 would work well.  Again, more power than you need but will offer transparency and detail without drifting bright.  This amp is $6495 new.  For perspective, I have customers driving Magico A3s and Martin Logan 13As with this amp.  Both tough to drive, brighter speakers. 

Pass is an obvious choice.  I think the INT-60 would be the model to go with.  Pricey at $9K new, these show up in the used market from time to time simply because it is such a popular brand. 

Naim Supernait 3 might also be a good choice.  I am not a fan of how it looks, but Naim gear tends to sound good.  This is a strong value at $4990 and delivers 80w of power. 

Full disclosure, I am a Musical Fidelity and AVM dealer.  Both are available with 30 day in-home demos.  I have no affiliation with any of the other brands.