System advice

@carlsbad2 thanks! Do you really think it would be ok to start with a dac and fit a proper amplifier to it later, not the other way around? Answering to your questions:

2) none of them are upgraded to engine 11, so in both cases I’d consider an upgrade in some future, however I think it could be a deal breaker because older Lampizators use r2r ladder and from what I know engine-11 brings sigma-delta to all of them. did you have by any chance an opportunity to to compare your GG to Big7? I wonder how huge the difference is.

3) I’m looking only at SE.

4) I’d like to connect a streamer to the DAC via USB and my CD player via S/PDIF or RCA if possible.

@soix thanks for your reply! I haven’t been able to put the Arcam gear back in - an input for spades has broken and I have to take it for a repair first. I don’t have any dedicated dac, I used only Naim CD player with internal dac to play music from my cd collection. Thanks for letting me know your concern about Ayon, I’m also fretting about it a little. Do you think my speakers with efficiency 88 dB may be difficult to drive by Ayon’s 2 x 30 W?

"What specific improvements are you looking for over what you’re hearing now?" - It’s a great question. I really should play Arcam first and then have something to refer to. But the issue is that the auction with Lampi is happening now, the Arcam is broken and I penciled in a listening sessions at audio shop in a couple of days :-) Truth be told, It shouldn’t be difficult to level up from my current audio equipment as it’s from previous century (however my attempts with Naim don’t confirm that). I listened to some Ayon’s before and the sound was vivid, warm, euphoric and I liked it  but didn’t have a chance to try other genres like rock and electronic music... I also tried some Chord stuff like Hugo but it wasn’t for me - it was too sterile.

It’s good that you really appear to know what you like. If your Arcam stuff is that old I’d upgrade the pre/amp first and get that right because it may affect which direction you might wanna go with a DAC, and there will be other used Lampi DACs available in the future if that’s where you end up wanting to go so there’s no real need to rush on that important decision. And yes I’d be hesitant to drive your speakers with a 30W amp, but you can try it with your music at the dealer and see. If I’m you I’d give that Octave a serious listen and if you like it (or the Ayon) borrow it and see what it sounds like at home, but I have a feeling that might be a great match for your tastes and speakers. And again, once you have that sorted then see which direction you wanna go sonically with a DAC. Getting a DAC now would be a big shot in the dark at this point, which is why I’d wait on that. Just my $0.02 FWIW.

@soix I'm not 100% sure if I know what I like. I know what I DON'T like: cold and sterile sound. Otherwise, I prefer everything what's good - dynamics. resolution, realism, wide sound stage, good bass, great midrange and a bit of sweetness and warm that makes it more magical experience ;-) Is is that much? 

UPDATE!

I had today a listening session at audio shop. I took my friend with me to compare the feelings. I had my piece of the equipment - Monitor Audio Platinum PL II speakers and XLO Signature 2 cables. We tried them against Ayon Crossfire III (SET) and Octave v80 (push pull). Ayon sounded surprisingly weak, bright and I didn’t like it at all. It was much better with Octave. But after some time we both found out that there is still something unpleasant with the sound that makes you tired of listening - a metallic glow. That was the moment where I unfortunately realized that my problem is my speakers...

We took Dynaudio Contour 20i and connected those speakers to Octave v80 SE and momentarily the metallic glow disappeared. There was more music, more fun, music was quite enjoyable. My friend was very satisfied. I was too for a moment, but... to be honest, I wasn’t delighted. My Monitor Audio speakers apart from having this metallic glow, have very detailed, nicely contoured sound which I like or I got used to it. At the same time Dynaudio Contour 20i give lot of fun, but the sound is kind of cloudy. Does it make any sense?

Anyway, this took me to the conclusion that I probably should start with changing my speakers. Maybe new ones will fit well with my Naim/ Arcam set? There's higher model of Dynaudio - Confidence 20, but I'm not sure if it's good way for me.

If so, what would be your recommendations?

Upon reading some reviews of your speakers I can see why there could be an issue with glare or an over abundance of detail in the upper mids and treble and may be what you’re hearing.  You could try these Joseph Audio Pulsars (original version) that could be much better/more refined in that area but not lack for transparency like the Dynaudio speakers — best of both worlds of you will.  If you buy well and they don’t work out for some reason you should be able to sell them for little/no loss so not a lot of risk, but I’d bet on you keeping them.  Just one idea FWIW. 

https://www.ebay.com/itm/186915696094