Warm, rich, smooth, 3d tube integrated amp, budget $6000

@facten Thanks!.  @smodtactical, you would be well advised to take this into account in making your selection among the many makes and models recommended.

So maybe this is the wrong path and I should go back to my prior idea of a warm tube preamp to replace the ARC?

My Haydn is 4 ohm, 25-180 watts is the recommended range and it seems to play well with 9.2 watts of my elekit tu8600. So maybe 40-60 watts will be enough for my use case?

If the Elekit works well, I would expect a 40-60 watter is a viable candidate.  I understand you don’t want a built in DAC, but it would be a mistake to not consider the Synthesis A40; I would take it over any other candidate even if it had no DAC.  It is better, for my taste anyway, than anything I’ve heard from any other company up to at least twice its price.  It’s sound is rich, harmonically saturated and weighty, without being murky or dynamically polite.  

I have owned several flavors Audio Research Pre and power amps and decided during covid to find something with a quality headphone output... Along with my wife's wishes that I use headphones so she can go about her own interest without listening to mine...

 Enter the Prima Luna Evo 400... Initially it sounded much more warm, with a smaller soundstage than my ARC gear (using Olympica II speakers) however, as it started to burn in I found it to keep getting better and better and after about 300hrs it became totally engaging and musical in every way...

As an experiment I then rolled in several of the upgraded British Bremer NOS tubes from Upscale Audio in the front end and finally settled on two French made tubes from Upscale in the central tube location with the Brimar moved to the next outer socket... Result...Absolutely amazing, sweet, 3d and fully engaging.  One less cable on the system too as I have gone from separates to an integrated.

Takes up less space than my ARC gear which I will be listing here in the near future. Except for my ARC Ref 9 CD.

So far as heat dissipation goes... Yes, 8 of those sweet EL34's create heat however not more than my previous ARC Ref 5SE and D135 amp.  I love the optional ability to roll in some output tubes at some point too.... I suspect If you were to buy a unit from Upscale or your local dealer II believe they may have a return option that is flexible... Considering that this unit weighs in over 50lbs... Heavy!

In my opinion... There is no substitute for a home audition with your other gear and room acoustics. 

Good luck with your search, enjoy the music!