Moving coil with a bit less leading edge

What about cartridges like:

47 Labs McBee
Yamamoto YC-03s
EMT TSD15 or JSD5
Miyajima Shilabe

Pani...You might be interested in going to the site known as 10 Audio and reading Jerry Siegel's detailed reviews of the Miyajima Shilabe and Miyajima Kansui cartridges. I found them quite interesting.

Is there something about AlNico magnets that all cartridges that use them normally tends to be "musical" ?

You will certainly get a more rounded, less edgy sound with a non-stone Koetsu (i.e., not the jades, or coralstone, etc). But, that comes with some woolly quality and overly prominent (and slow) upper bass.

I like Allaert cartridges for a smoother and refined sound while not giving up too much in dynamics.

Syntax raised a good point about cartridge arm compatibility. The Lyra cartridges have metal bodies designed to convey vibrational energy from the cartridge body into the arm for the arm to dampen/dissipate. The arm must be well designed for that task to get the most out of those cartridges. In some threads, Jonathan Carr, the designer of Lyra cartridges mentions some arms he considered well up to the task (sorry I cannot remember which arms are mentioned).

Pani,
I hope you will get to try your Lyra Delos on a better tonearm than stock Technics SL-1200 direct drive table. Don't even think about Shilabe with that arm.