Magico needs warm, slightly laid back ss amps with good power, or some tubes in the mix to sound their best imho. Though I heard the new Boulder 1100 series amps with the S3 Mk2's recently & thought that was a really good match. Personally my favorite ss amp for synergy is Vitus Audio, however they’re not cheap.
With your S1’s, I think the Aesthetix Atlas might sound a bit ’thin’. The BHK stereo amp could be a good match; it’s basically like a more refined CJ Premier 350SE.
However, my advice to you would be upgrade your speakers before amplification. The reason for that is loudspeakers have the greatest influence on the sound of your system. And the S1 Mk1’s are not that good to be honest. The S1 Mk2’s are a LOT better. However, in your shoes I would sell my S1’s and order a pair of A3’s which are a really nice speaker. The A3’s will be better across the board, especially the bass & present an easier load to the amp. My 2c.