BAT amp + cheap pream vs BAT integrated vs Prima Luna integrated

I think there is a lot of gear out there that will make you happy.  You have narrowed to two items.  I have no opinion on that PrimaLuna. I have not heard it and have only heard older models. 
 

that said with BAT, pairing with an inexpensive preamp is a terrible idea. In fact, with BAT, assume you almost have to pair it with BAT to get the most out of it.  I am not a BAT dealer but have had multiple items in on trade including an amp, preamp, phono combo and testing each piece individually I thought it was awful.  Out of curiosity I set them up together and made a huge difference.  I know it will work with other brands but that hear has to have correct electrical properties AND be fully differentially balanced.  
 

I am not saying get primaluna, just don’t get a BAT and off brand pre.  
 

You have told us about your speakers and a little about your likes and dislikes but I am not understanding your listening habits, room size, types of music you listen too, etc…. Also, what kind of phono stage.  MM and MC or just MM.   something like an Audia Flight FLS 9 w/ phono might be perfect for you but need to know more about music taste, etc…
 

one thing that does seem clear is you do not like a cold sound.  Steer clear of SoulNote as it will likely not be to your taste.  It is wonderful gear, but will be a bit colder.  
 

Whoever told you older gear will not sound as good as newer is absolutely full of crap. Also the dealer who said BAT sounds awful is also.  I've owned several pieces of BAT. Good stuff. To reiterate above,  buy the best preamp you can.  You may also want to consider Audio Research line.  Not sure it's a good match with ATC though. Separates will sound better this i do know unless its really high dollar integrated.  

Again, buy the best preamp you can :)

@samzx12 thank you for pointing out my poor phrasing.  That is what I get for typing something in the middle of the night with Insomnia.   
 

the BAT gear I had was dreadful mixed into my system at the time.  I stand by that.  When I put the whole system together though, I was not clear that it did not just get better which is what I said, it was fabulous.  I was not clear on that and I do pride myself on being helpful and clear.  Thank you for prompting a correction. BAT gear is legit, superb.
 

that said, I think my experience is valid in that i have also found it slightly harder to pair and match with other brands gear and that gear needs to be balanced.  I firmly believe a Schiit Freya with a BAT amp is a bad option.  To get most out of it, something balanced is required.  

Hi guys, Just my 2 cents worth.  I have owned a Ton of gear literally maybe 5 tons, lol.  I have auditioned the ATC Speakers at Audio Connection in Verona, NJ.  The ATC SCM40 were my Fav's he powered them with an Audio Research I50 integrated and it drove them beautifully.  So people saying you need a lot of power and SS to drive them adequately is in my opinion not accurate.  I did also listen to them with Aesthetix Dione's at 3.5x the power and the overall sound was also pleasing.  Minor difference was in tighter bass but at a cost of less midrange texture.  But great soundstage with both.  I will put a list of my amps at the bottom of this post to try to validate my post.  My recommendation would be to get a used Bat VK52se for about $3500 and a used Vk655se for about $5500 both preferably with Gen 3 caps boards, that will set you back $9k.  I have seen both sold at those prices.  Matter of fact a VK53se w/ Gen 2 caps was sold for $3500 recently.  I will get to the phono latter.  If you truly want tubes you can find a pair of Vk150se's right now for $6k.  Still within you budget.  Now for the best part, to make the most holographic and accurate sounding system you can upgrade the output caps to VCap ODAMs in the Preamp and CUTF's in the Amp and OMG.  I have gone from a Vk51se to a Rex to a Vk53se(Gen 3) to now a Rex3(VCap) and each step was incredible.  2 of my friends have my former gear and they feel they have reached their dream system.  My Amp upgrades were similar.  I went from 2 pair of vk150se (paralleled 300wpc) to a pait Vk600mse to a a pair of Vk655se(Gen3) to a Rex500 (Gen4).  Totally in my Dream space!  As for the phono pre you can start at $1k with a Graham Slee Acession or a Project DS2 Tube Box to start and up grade later.  Check me listings for my contact info if you would like to reach out.  Here is my list of amps that I have owned.

My Amps

Adcom GFA 555
Adcom GFA 585
Accuphase A50
BAT Vk500
BAT VK6200 pair multichannel (2units) 
BAT VK 600se
BAT VK 600mse pair Mono
BAT VK 655se pair Mono Gen3
BAT Vk 655se Gen2
BAT VK 150se 2 pair Mono
BAT VK 55se mono pair
BAT Rex500 (CURRENT)
Boulder 500ae
Boulder 2060
Bryston 4B 
Bryston 28BSST mono pair
Cary SLM200 pair mono
Cary 805c pair mono
Cary 805ae pair mono
Cary 211m pair mono
Cary 1610 pair mono
Cary 300bse sig pair mono
Classe Ca 101
Classe CA 201
Classe CA 301
Classe CA 401
Classe CAV500 multichannel
Classe Omega Omicron
Classe Omega Reference Stereo 2 pair
Classe Omega Reference Mono's 5 total amps (Orig early manufacture)
Classe Omega Reference Mono pair (CURRENT, last year of manufacture)
Conrad Johnson Premier 8a 2 pair mono
Conrad Johnson Premier 11a pair Stereo
Counterpoint SA220 pair stereo
Counterpoint SA 4 OTL/OCL pair mono
Crown Power Line 2
Crown Studio Reference I 
Crown MacroTech 2400
Crown MacroTech 3600vz
Crown K1 3 Stereo/mono (2 active 1 spare CURRENT HT)
Crown K2 4 stereo/mono (2 units CURRENT)
EAD PM7300 pair multichannel (2 units)
EAD PM1000 multichannel
Emotiva XPA-9 Gen3 (CURRENT HT)
Golden Tube Audio SE40 pair stereo
Golden Tube Audio SE100
Jc Verdier 845 luxe  pair mono
Joule Electra Rites of Passage OTL pair mono
Joule Electra Destiny OTL pair mono  (CURRENT)
Kenwood L-07m pair mono
Krell KMA 100 pair mono
Krell 750mcx pair mono
Krell Chorus 7200 multichannel
Krell Evo600 pair mono
Krell Evolution One pair mono
Lexicon GX7
Melos MAT1000 3 pairs mono
McIntosh mc30
McIntosh mc302
Nakamichi PA7 pair stereo
NAT Audio Magma New pair mono
NAT Audio SE1 pair mono
Pass Labs X600
Pass Labs XA200.5
Pass Labs Aleph (4 in Active Rushmore Speakers)
Phase Linear 1000
Plinius Sa250 mkV
Plinius Sa103
Sunfire Cinema Grand Signature
Carver Silver Seven T
Carver Cube
Threshold T800D pair Stereo
VAC 140 (70/70) pair mono
Viva Verona XL pair mono
Yamaha B1 pair mono
Wavac 833 pair mono
Benchmark AHB2

VIP428, I think you should try some more amps before you offer your opinion here !   Seriously, that’s a lot of amps!

OP, I think the best advice here you’ve received is to figure out which speakers you will buy next before investing in a new integrated.  Synergy is really important.  Making one change in a system often leads to changing out most or all of the rest of the system.  That’s one reason so many of us have owned so much different gear.  Lastly, find a good trusty dealer - they often have figured out this synergy thing a long time ago with the components they sell.