Thanks for all the very helpful insights and comments! Based on those and other information, I ended up with the Hegel H95. Class A amplifiers were very tempting, but pricey and didn't fulfil the requirements for ease of use. Finally, it came down to Naim and Hegel, but the Naim was supposedly the more aggressive of the two. The H95 was also described as smoother and having less leading edges on notes than the H120 or H190 for instance, which seemed to go in the right direction.
I'm really surprised by how smooth the sound is with the Buchardt S300 mkII, especially out of the box and even with the internal DAC, which is known to be rather bright and Chord-like. It's a completely different experience from the Arcam SA20 and, of course, the Rogue Sphinx. I wonder if part of the smoothness comes from the lower power (60W vs. 90W and 100W respectively) and whether the Arcam is more aggressive than I thought it was compared to other amps. Very dynamic recordings can still have transients that are slightly hard for me (e.g. snare hits) and some harsher frequencies are at times present, but I can totally live with those.
In general, it's evidently not as smooth, rich, full, 3D and mellow as the PrimaLuna in triode mode, but I was very impressed by the sound quality of the Hegel. Detailed, engaging, lifelike, very good soundstage, not stuck to speakers, beautiful spatial cues, etc. It doesn't project voices for instance in front as some do (including the Arcam and Rogue), but everything is very nicely separated and you can focus on the different instruments and voices easily.
Based on my experience, I can recommend the H95 for those having trouble with fatigue or finding amps too bright or aggressive. I have no experience on what happens once you go up the line, especially if you have sensitive speakers, but from what I've gathered, in terms of transient energy, leading edges as mentioned above, and slam, you will get a less smooth and mellow experience. However, I am curious to hear the H190, and especially the H390, even though I'm more than happy with the entry-level model and not planning to upgrade anytime soon!