Primaluna or not Primaluna

I heard good things about this one:

https://www.lab12.gr/product/integre4-mk2/

Tube/valve amps vary so much depending on what they're driving, particularly the SET variety. It is a challenge to get adequate driving power esp for rock from SETs (except perhaps exotic megabuck varieties). I think compromise is always involved - liquidity, transparency, holography and warmth of SET vs punch +/- volume of push-pull. interestingly while I love the SET sound for hifi listening, my Mesa guitar amp allows switching from 50w push pull to 5W SET. Even playing at similar volume settings I MUCH prefer playing through the Pushpull setting. Strange that I have loved SET so much in the hifi. I think it might be the holographic stereo soundstage and transparency which is so allluring.
 

Not sure you should rate ability to tube roll so highly in your priorities as that may limit your options of achieving the sound you're after. At the end of the day you're likely to settle for one of the tube options after some experimentation. 
the compromise I reached was with Audion Black Shadow 845 monoblocks. Pure Sound, Unison Research and other manufacturers also make amps with the 845 valve - might be query looking to see if anyone does an integrated using the 845. Being originally designed for transmission it has more oomph than most other SET designs. Mine drive a pair of Coincident Super Eclipse. 23 foot x 13 ft room. Volume levels not a problem. The only thing I've trialled in my system which I was tempted by was a pair of JE Audio push pull monoblock. It traded just a small amount of the SET magic for more punch on bass drum, snare etc. 
Best wishes for your search. 

In your shoes i'd get the hardwired Audion Sterling with a pair of Zu Audio Omen book shelves. The entire set up for around $4200.

98db, 35lb speakers that will beautifully coincide with what the Sterling offers.

Several of your sugestions is not availeble in Sweden (where I live). If I was in the US it would be pretty easy to order an amplifier from some small interesting brand and have the option to return it in, say, 60-days, if I don’t like it. That will not be so easy when living in Sweden. And if I took a chance and order a amp for $4000 it would be $5500 when I would receive it due to tax and fees.

Yes, there are always other amlifiers that sounds better. Even if I buy one for 10k there will be better ones.

I gladely loose some detailand sound stage to a sound that engages me, makes it fun to listen to the music and makes me forget analyzing everything. Rather a presentation that alows me to listen to more that 50% of my CD:s and LP:s without beeing disturbed by harsh and thin sound. With other words; it’s OK if the sound is a bit more warm and forgiving than being neutral and analytical.
I want an amplifier that seduces me with the music, not just giving me the biggest sound stage, all the details and the truth and nothing but the truth.

I remember when I was a teenager and I just was listening to the music and never had any thougts about how detailed or reveiling or.... the sound was. I was just embraced by the music.
I know I will never find my way back to when the music was everything and I never though much about the details of how the presentation.
When I bought my first "upgrade", then the hunt for better sound started.
Maybe 14 years as a mastering engineer ”destroyed my simple way” of listening too.

Problem is that I bought a tube amp several years ago (Tube Technology Unisis Signature with EL84 tubes) and fell in love with the ”tube magic”.
If it hadn’t been for for a bad PCB-card I would surely have used it today.
Bought a solid state amp, Musical Fidelity M6, but never really liked it.
Bought a Line Magnetic LM-34AI and never really liked it.
Bought an Audion Audio Sterling and really liked it, but the problem was the measly 12 watts.
So now I have a pile of tubes I want to use (EL34, KT88, 6550, 6922, ECC81, ECC82, ECC83, E88CC…).

And here I am today, struggeling to find the best partner to my
speakers...sigh.

Many thanks to you all for all the input.

It might be difficult to find preowned but a Leben CS600 or CS600x would check your power tube wants. Since you are desirous of rolling tubes, the Primaluna might be your best option given ease of rolling and adaptive auto bias. For best sound you might consider buying the amp for sound quality/match with your Tannoys and sell off the tubes.

A preowned Audio Note UK integrated might be all you need to match up well with the Tannoys and a Soro se sig used would slot into your price range. Once again, you fell in love with the tube sound when experimenting with an el84 based amp. Why not consider a preowned Audio Note OTO SE Sig or Leben CS300xs. Many of us here who have fallen for tubes over the years fell for the el84. I’ve spent alot of time and money over the years chasing ever more up the vacuum tube food chain. I have found it but it comes at a considerable cost. If I had stopped at the Leben cs300x/cs300xs 15 years ago I could own a small country with what I’ve spent since.